HUG, Circuit Judge:

Stanley Williams, a prisoner on California’s death row, appeals the district court’s denial of his 28 U.S.C. § 2254 habeas corpus petition challenging his 1981 conviction of multiple counts of first-degree murder and armed robbery and his sentence of death. Williams also appeals the district court’s denial of his motion, made under Federal Rule of Civil Procedure 60(b), for relief from the court’s judgment denying his habeas corpus petition. For the reasons set forth below, we affirm the district court’s denial of Williams’s habeas corpus petition, and we vacate the district court’s order denying Williams’s Rule 60(b) motion because the district court lacked jurisdiction to consider the motion.

FACTS AND PROCEDURAL HISTORY

I. The Trial.

On May 3, 1979, the state of California charged Williams with four counts of first-degree murder, three counts of robbery with the use of a firearm, one count of kidnapping, and eight special circumstances of robbery-murder and multiple murder. Williams’s trial commenced on February 10, 1981. We respectfully take the following account of the trial, in large part, from the California Supreme Court decision in People v. Williams, 44 Cal.3d 1127, 245 Cal.Rptr. 635, 751 P.2d 901, 905-08 (1988) (en banc) (“Williams /”). We provide additional facts in the discussion, below, as necessary for consideration of Williams’s claims for relief.

A. The Prosecution’s Case.

The state presented evidence linking Williams to two separate incidents of murder and robbery. See Williams I, 245 Cal.Rptr. 635, 751 P.2d at 905-07.

1. The 7-Eleven Murder and Robbery.

Alfred Coward, an immunized government witness, testified to the events leading to the murder of Albert Lewis Owens, 1 an employee of a 7-Eleven store in Whittier, California. See id. at 905. Coward stated that at approximately 10:30 p.m. on February 27, 1979, Williams dropped by Coward’s house. The two men then went to James Garrett’s house, where Williams was staying. Only Williams went inside, returning with a sawed-off shotgun and accompanied by a man named Darryl. The three men made several stops, including one to obtain “Sherms,” cigarettes containing phencyclidene (“PCP”). After sharing a Sherm, the three picked up Tony Simms. Williams then had a second Sherm with Coward and Simms, and asked Simms if he knew where they could “make money.” See id.

Coward testified that, taking two cars, the four men made two unsuccessful restaurant and liquor-store robbery attempts. Subsequently, they went to a 7-Eleven where Owens was sweeping the parking lot. Simms and Darryl went into the store, followed by Owens, Williams, and Coward. Williams, the only one with a weapon, approached Owens and ordered *579 him to keep walking. Owens walked toward the back rooms of the store with Williams and Coward following him. Williams instructed Owens to lie down, which he did. Williams shot out the store’s television monitor and then shot and killed Owens. See id.

According to Coward, the four men returned to Simms’s house where they divided among them the $120 that they had taken from the 7-Eleven cash register. When Simms asked' Williams why he had shot Owens, Williams responded that he did not want to leave any witnesses. He also said that the shotgun shells could not be traced, and that he had retrieved a few of them. See id.

Coward saw Williams later thát morning at Williams’s brother’s home. Williams told his brother about Owens, saying: “You should have heard the way he sounded when I shot'him.” Williams then made a growling noise and laughed hysterically for a number of minutes. See id.

2. The Brookhaven Motel Murders and Robbery.

Robert Yang and his family lived in and owned the Brookhaven Motel on South Vermont Street in Los Angeles, California. At about 5 a.m. on March 11, 1979, Yang heard a woman’s screams and three or four shots. A few minutes later, he left his bedroom and saw that the door separating the motel office from the family’s living quarters was ajar. The door seemed to have been forced open from the outside. Yang discovered his father, mother, and sister, all fatally wounded from shotgun fire. The cash drawer was open and empty. See id. at 906.

The police found two shotgun shell casings at the scene. A firearms expert testified that one of the shells could only have been fired from a weapon that Williams had purchased in 1974. See id.

Four witnesses provided testimony identifying Williams as a perpetrator of the Brookhaven Motel murders and robbery. Samuel Coleman, testifying as an immunized government witness, stated that on March 10, 1979 he and Williams went to the 'Showcase Bar, where Coleman remained until it closed around 6 a.m. Coleman last remembered seeing William's at about 2:30 a.m. The next day, Williams told Coleman that he had robbed and killed some people on Vermont Street. Williams said that he had obtained approximately $50 from the robbery-murder and was going to use it to buy PCP. See id.

James Garrett testified that Williams kept some of his possessions at the Garrett house and stayed there approximately five days, a week. Early on the morning of March 13, 1979, Williams told James Garrett and his wife that he had heard of the killing' of some “Chinese people” on Vermont Street. Williams said that he' did not know how the murders had occurred, but thought that the murderers were professionals because they had left no shells or witnesses at the scene. Williams also stated that he had heard that the killings had taken place at 5 a.m., and that two men had knocked down the door and -taken $600. See id.

Williams later spoke to James Garrett a second time about the Brookhaven Motel murders and robbery. Williams described the incident, saying: “[AJffcer the big guy knocked the door. down, he went in the motel, and there was a guy laying on the couch, and he blew him away.” Williams said that the man on the couch and a woman at the cash register were shot twice, and that another woman was also shot. James Garrett testified that Williams then indicated that he was the “big guy.” See id. 2

*580 Esther Garrett confirmed the statements made by her husband. She testified that Williams informed them that the Brookhaven Motel murderers were using the money taken from the cash register to buy “juice,” or PCP, and that they had picked up the shotgun shells so that there would be no evidence for the police. Williams also told Esther Garrett, outside the presence of her husband, that he, Williams, had committed the murders with his brother-in-law. See id.

George Oglesby, an inmate housed in the same cell block as Williams, testified that Williams admitted to shooting a man, a woman, and a child in the course of robbing a motel. See id. at 906-07. Oglesby also testified in detail to Williams’s plan to escape from jail. Williams had invited Oglesby to participate in the plan, which was complete with drawings and involved an escape during a bus transfer from jail to court. See id. at 907. Two persons outside of jail were to disarm the officer driving the bus, and then Williams was to kill the person on the bus who planned to testify against Williams, as well as the two officers accompanying the bus. Williams later modified the plan to include blowing up the bus in order to prevent the authorities from quickly determining who had escaped. See id.

After receiving two notes from Williams relating information about outside participants in the escape plan, Oglesby informed Lieutenant Fitzgerald of the planned escape. Williams subsequently sent Oglesby more notes discussing the escape. See id.

The initial target date for the escape was June 12, 1979. However, Williams aborted the escape attempt planned for this day because he could not ensure that he and Oglesby would be transferred to court at the same time. In addition, after one of his court appearances, Williams informed Oglesby that the escape attempt had to be cancelled because Williams believed that two police vehicles had followed the bus transporting Williams between jail and court. Williams then altered the escape plan so that the escape attempt would occur after they left court. See id.

B. The Defense.

Williams presented an alibi defense. Beverly McGowan testified that she and Williams had dined and spent the night together on February 27, 1979, the night of Owens’s murder. See id.

Fred Holiwell, Williams’s stepfather, testified that he arrived at the Showcase Bar at around 3:30 a.m. on March 11,1979, the morning of the Brookhaven Motel murders and robbery. He stated that he thought he saw Williams in the Showcase Bar parking lot area at about 5 a.m. Holi-well remembered seeing Williams at the Showcase Bar on this particular night because Williams had been involved in an altercation that resulted in a cut across Williams’s chest. See id.

Eugene Riley, an inmate in the same cell block as Williams, testified that he saw Williams in the parking lot of the Showcase Bar at about 5 a.m. on March 11, 1979. Riley gave Williams a ride home at approximately 5:30 a.m. and said that Williams was smoking a Sherm at the time. See id.

Joseph McFarland, another inmate in Williams’s cell block, provided testimony impeaching Oglesby’s credibility. McFarland stated that Oglesby was a well-known “jailhouse rat,” and that other inmates gave Oglesby false information because *581 they knew him to be a government informant. See id. at 907-08. ■ ■ Through the use of cross-examination, defense counsel also brought out the motivations of the prosecution’s witnesses to he.

C. The Jury Verdict.

On March 13, 1981, the jury returned guilty verdicts against Williams on four counts of first-degree murder and two counts of robbery using a firearm. 3 The jury also found to be true the eight special circumstances of robbery-murder and multiple murder. Following a penalty phase, at which neither the prosecution nor the defense put on any evidence, the jury returned a death sentence. On April 15, 1981, the trial court imposed a judgment of death.

II. The Appeal and Post-Conviction Proceedings.

Pursuant to California’s 1978 death penalty law, Williams’s conviction and sentence were automatically appealed to the California Supreme Court. While the appeal was pending, on June 25, 1984, Williams filed a state petition for a writ of habeas corpus, which was consolidated with his direct appeal. See id. at 905. The California Supreme Court ordered an evidentiary hearing on issues raised in the habeas corpus petition. An appointed referee conducted a five-day hearing and made factual findings on the issues of whether (1) Oglesby was a government agent that deliberately elicited incriminating statements from Williams in violation of the Sixth Amendment, (2) Oglesby was a government agent that interrogated Williams in violation of the Fifth Amendment, and (3) Williams’s trial counsel was ineffective for failing to object to Oglesby’s testimony under the Fifth and Sixth Amendments and. correlative provisions of the California Constitution. See id. at 908. On April 11, 1988, the California Supreme Court issued an opinion affirming Williams’s conviction and sentence and denying his habeas corpus petition. See id. at 921. The .California Supreme Court denied Williams’s petition for rehearing, and the United States Supreme Court denied his petition for a writ of certiorari. See Williams v. California, 488 U.S. 975, 109 S.Ct. 514, 102 L.Ed.2d 549 (1988).

On January 9, 1989, Williams filed a second state habeas corpus petition, which the California Supreme Court summarily denied. Williams filed a federal habeas corpus petition in the United States District Court for the Central District of California on January 23, 1989. The district court ordered the petition held in abeyance pending exhaustion of all of Williams’s claims in state court.

On September 1, 1989, Williams filed a third state habeas corpus petition with the California Supreme Court, which ordered another evidentiary hearing on the question of whether the prosecution used Oglesby as a government agent in violation of Williams’s Fifth and Sixth Amendment rights. See In re Williams, 7 Cal.4th 572, 29 Cal.Rptr.2d 64, 870 P.2d 1072, 1074 (1994) (en banc) (“Williams II”). After the second hearing and a post-hearing briefing, the California Supreme Court issued an ■ opinion on April 11, 1994 that denied the habeas-corpus petition. See id. at 1095. The Court also denied Williams’s petition for rehearing. On June 21, 1995, the California Supreme Court denied Williams’s fourth and final state habeas corpus petition on the merits and on procedural grounds.

*582 After exhausting his claims in state court, Williams filed with the district court an amended federal habeas corpus petition on November 13, 1995. Granting, in part, the state’s motion for summary judgment on March 27, 1998, the district court denied twenty-four of the twenty-eight claims raised in Williamses amended federal petition. See Williams v. Calderon, 48 F.Supp.2d 979, 1032 (C.D.Cal.1998) (“Williams III”). On May 27-28, 1998, the district court held an evidentiary hearing, at which witnesses were called and exhibits submitted, on Williams’s claims that he was unconstitutionally shackled at trial and that his trial counsel rendered ineffective assistance in violation of the Sixth Amendment. See Williams v. Calderon, 41 F.Supp.2d 1043, 1046 (C.D.Cal.1998) (“Williams IV”). The district court issued an opinion denying Williams’s remaining claims on December 21, 1998, see id. at 1060-61, and entered judgment accordingly on December 23,1998.

On January 8, 1999, Williams filed a motion asking the district court to amend its findings of fact and judgment under Federal Rules of Civil Procedure 52(b) and 59(e). While the motion to amend was still pending, on January 22, 1999, Williams noticed his intent to appeal the district court’s December 23, 1998 judgment and also requested a certificate of probable cause (“CPC”) in the event that the district court denied his motion to amend. On May 21, 1999, the district court did deny Williams’s motion to amend, but granted his application for a CPC to appeal the denial of his federal habeas corpus petition. Williams filed an amended notice of appeal on June 3, 1999, indicating his intent to appeal the district court’s order denying his motion to amend.

On November 17, 1999, Williams filed with the district court a motion for relief from judgment under Federal Rule of Civil Procedure 60(b), which the district court denied on December 17, 1999. On December 29, 1999, Williams noticed his intent to appeal the district court’s order and requested a CPC for this purpose. The district court denied Williams’s request on January 28, 2000. On February 10, 2000, Williams filed an amended notice of appeal, which we treated as an application to this court for a certifícate of appealability (“COA”). On May 5, 2000, we granted a COA limited to the issues raised by the district court’s denial of Williams’s Rule 60(b) motion.

JURISDICTION

We first consider our jurisdiction over Williams’s appeal of the district court’s judgment denying his habeas corpus petition, No. 99-99018, and then of the district court’s order denying his Rule 60(b) motion, No. 00-99001.

I. The Habeas Corpus Petition.

The district court had jurisdiction over Williams’s habeas corpus petition under 28 U.S.C. § 2254. Williams filed a timely notice of appeal of the district court’s December 23, 1998 judgment denying his petition. Williams’s motion to amend under Rules 52(b) and 59(e), timely filed ten days after entry of the judgment, see Fed. R.Civ.P. 6(a), 52(b), 59(e), tolled the time to file his notice of appeal until May 21, 1999, when the district court issued its order denying the motion. See Fed. RApp. P. 4(a)(4)(A). Williams’s January 22,1999 notice of appeal also became effective on May 21, 1999, when the district court denied his motion to amend. See Fed. R.App. P. 4(a)(4)(B)(i); see also Schroeder v. McDonald, 55 F.3d 454, 458 (9th Cir.1995). Accordingly, Williams’s notice of appeal was timely. See Fed. R.App. P. 4(a)(1)(A) & 4(a)(4)(A).

*583 The CPC that the district court granted, however, is not sufficient to confer jurisdiction on this court to review the district court’s denial of Williams’s habeas corpus petition. Because Williams filed his notice of appeal after the effective date of the Anti-Terrorism and Effective Death Penalty Act (“AEDPA”), the AEDPA’s provisions govern his right to appeal. See Slack v. McDaniel, 529 U.S. 473, 478, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). Under ' the AEDPA, we cannot review a district court’s final order in a habeas corpus proceeding without a COA, for which the petitioner must make “a substantial showing of the denial of a constitutional right” on each claim appealed. 28 U.S.C. § 2253(c); Mayfield v. Woodford, 270 F.3d 915, 921-22 (9th Cir.2001) (en banc). Because Williams could not have known that he needed a COA, rather than a CPC, to appeal the district court’s denial of his habeas corpus petition, see Morris v. Woodford, 229 F.3d 775, 779 (9th Cir.2000) (noting that before the Supreme Court’s decision in Slack, the rule in this circuit was that the AEDPA’s provisions did not govern petitions filed in the district court before the AEDPA’s effective date of April 24, 1996), we treat his notice of appeal as an application for a COA on the issues raised in his opening brief. See Cooper v. Calderon, 255 F.3d 1104, 1107 (9th Cir.2001); Schell v. Witek, 218 F.3d 1017, 1021 n. 4 (9th Cir.2000) (en banc).

The AEDPA’s “substantial showing” requirement for a COA is “relatively low,” Jennings v. Woodford, 290 F.3d 1006, 1010 (9th Cir.2002), and is satisfied when the “petitioner can ‘demonstrate that the issues are debatable among jurists of reason; that a court could resolve the issues [differently]; or that the questions are adequate to deserve encouragement to proceed further.’” Id. (quoting Barefoot v. Estelle, 463 U.S. 880, 893 n. 4, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983)). “Although not dispositive, ‘[i]n a capital case, the nature of the penalty is a proper consideration in determining whether to issue a certificate of [appealability].’ ” Lambright v. Stewart, 220 F.3d 1022, 1025 (9th Cir.2000) (quoting Barefoot, 463 U.S. at 893, 103 S.Ct. 3383); see also Mayfield, 270 F.3d at 922. We resolve any doubt about granting a COA in the petitioner’s favor. Jennings, 290 F.3d at 1010; Mayfield, 270 F.3d at 922; Petrocelli v. Angelone, 248 F.3d 877, 884 (9th Cir.2001).

Under the foregoing standard, we conclude that Williams has made the requisite “substantial showing of the denial of a constitutional right” on all but two of the claims presented in his opening brief in No. 99-99018. The two claims that do not warrant a COA are those that allege the prosecution’s racially discriminatory use of peremptory challenges (Claim C), and the state’s deliberate interference with Williams’s confidential relationship with defense counsel and defense experts. (Claim AB)

Williams argues that under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), the prosecution impermissibly exercised peremptory challenges to exclude three African-American jurors in violation of the Equal Protection Clause. To establish a prima facie case, Williams must show that the facts and circumstances of the jury selection raise an inference of discriminatory exclusion by the prosecutor. See Batson, 476 U.S. at 96, 106 S.Ct. 1712. In his habeas corpus petition, Williams made only the following allegations regarding the facts and circumstances of voir dire: “The prosecutor used two of his nineteen peremptory challenges to remove the only two African-American females to be seated as prospective jurors .... He used one of three peremptory challenges to remove William Coleman, an *584 African-American male, from potential jury service as an alternate juror in petitioner’s case.” In opposing the state’s summary judgment motion, Williams failed to allege any additional facts or circumstances of the jury selection.

Although a pattern of strikes against African-Americans provides support for an inference of discrimination, id. at 97, 106 S.Ct. 1712, Williams must point to more facts than the number of African-Americans struck to establish such a pattern. We have previously ' stated that, “Using peremptory challenges to strike Blacks does not end the [prima facie] inquiry; it is not per se unconstitutional, without more, to strike one or more Blacks from the jury.... A district court must consider the relevant circumstances surrounding a peremptory challenge.” United States v. Vasquez-Lopez, 22 F.3d 900, 902 (9th Cir.1994) (citations omitted).

Statistical facts like a high proportion of African-Americans struck and a disproportionate rate of strikes against African-Americans can establish a pattern of exclusion on the basis of race that gives rise to a prima facie Batson violation. See Fernandez v. Roe, 286 F.3d 1073, 1078 (9th Cir.2002) {prima facie case when the prosecutor struck four out of seven (57%) Hispanics, and 21% (four out of nineteen) of the prospective juror challenges were made against Hispanics who constituted only about 12% of the venire); Turner v. Marshall, 63 F.3d 807, 813 (9th Cir.1995) (five of nine (56%) African-Americans struck, and 56% (five out of nine) of the challenges were made against African-Americans who constituted only about 30% of the venire), overruled on other grounds by Tolbert v. Page, 182 F.3d 677 (9th Cir.1999) (en banc). However, because Williams failed to allege, and the record does not disclose, facts like how many African-Americans (apparently men, if any) sat on the jury, how many African-Americans were in the venire, and how large the venire was, it is impossible to say whether any statistical disparity existed that might support an inference of discrimination.

Williams attempts to create an inference of discrimination by pointing to (1) two, unrelated California Supreme Court decisions that found the prosecutor of Williams’s case to have used peremptory challenges in a racially discriminatory manner in those cases, and (2) the prosecutor’s closing argument at trial, in which Williams argues that the prosecutor made a racist analogy, a claim that the district court rejected and Williams does not appeal. We find these circumstances irrelevant because they are not “the circumstances concerning the prosecutor’s use of peremptory challenges” at Williams’s trial. Batson, 476 U.S. at 97, 106 S.Ct. 1712. Even if we assumed some relevance, the cited circumstances are not sufficient to raise an inference that the prosecutor exercised peremptory challenges in a racially discriminatory manner in Williams’s case. Because Williams failed to present the district court with sufficient factual allegations to establish a prima facie case under Batsón, we conclude that he has not made the requisite “substantial showing of the denial of a constitutional right,” 28 U.S.C. § 2253(c)(2), and therefore deny a COA on his Batson claim.

We also decline a COA on Williams’s claim that jailhouse monitoring of his conversations with visitors, and the interception by jail personnel of a document indicating the appointment of Dr. Alvin Davis as a defense psychiatrist, violated his Sixth Amendment right to counsel. When the government deliberately interferes with the confidential relationship between a criminal defendant and defense counsel, that interference violates *585 the Sixth Amendment right to counsel if it substantially prejudices the criminal defendant. Clutchette v. Rushen, 770 F.2d 1469, 1471 (9th Cir.1985); Weatherford v. Bursey, 429 U.S. 545, 557-58, 97 S.Ct. 837, 51 L.Ed.2d 30 (1977). Substantial prejudice results from the introduction of evidence gained through the interference against the defendant at trial, from the prosecution’s use of confidential information pertaining to defense plans and strategy, and from other actions designed to give the prosecution an unfair advantage at trial. United States v. Irwin, 612 F.2d 1182, 1187 (9th Cir.1980).

Even if we assume that the jailhouse monitoring and document interception were deliberate state interference with the confidential relationship between Williams and his counsel, Williams fails to establish substantial prejudice. Williams does not argue, and the record does not show, that the prosecution used any confidential information obtained from the monitoring or interception to achieve an unfair advantage at trial. In fact, the record indicates that the prosecution was unaware of the document regarding Dr. Davis’s appointment until defense counsel brought it to the prosecution’s and the trial court’s attention. Rather, Williams contends that the monitoring and interception were prejudicial because they hampered his ability to present a defense of diminished mental capacity. Williams alleges that Dr. Davis refused to assist in the preparation of such a defense because the confidentiality of his appointment as a retained expert had been compromised, and because he was unable to obtain a confidential interview with Williams free of jailhouse monitoring.

The loss of Dr. Davis’s services did not substantially prejudice Williams. Criminal defendants have no constitutional right to a psychiatrist of their choice, Ake v. Oklahoma, 470 U.S. 68, 83, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), and the trial court had already appointed three other mental-health experts to evaluate whether Williams was diminished in capacity at the time of the alleged offenses. Moreover, to obtain a fourth psychiatric opinion, defense counsel could have replaced Dr. Davis with another mental-health expert and sought an order from the trial court permitting a confidential interview. Williams fails to make a “substantial showing of the denial of a constitutional right” due to the state’s jailhouse monitoring and document interception. See 28 U.S.C. § 2253(c)(2). We therefore deny a COA on Williams’s claim that such monitoring and interception violated his Sixth Amendment right to counsel.

However, we conclude that Williams has made the requisite “substantial showing of the denial of a constitutional right” on the remaining claims presented in his opening brief in No. 99-99018, which we consider below on an issue-by-issue basis. See 28 U.S.C. § 2253(c)(3). We hereby grant a COA limited to these claims regarding the merits of Williams’s habeas corpus petition. 4 We exercise jurisdiction over the claims pursuant to 28 U.S.C. § 2253 and Rule 22 of the Federal Rules of Appellate Procedure.

*586 II. The Rule 60(b) Motion.

We' review de novo the district court’s assertion of jurisdiction over Williams’s Rule 60(b) motion for relief from judgment, see Carriger v. Lewis, 971 F.2d 329, 332 (9th Cir.1992) (en banc), and conclude that the court lacked jurisdiction to consider the motion. Once Williams filed his notice of appeal of the .district court’s judgment denying his habeas corpus petition, the district court lost jurisdiction over the petition. See id.;. Gould v. Mutual Life Ins. Co., 790 F.2d 769, 772 (9th Cir.1986). To seek Rule 60(b) relief during the pendency of an appeal, “ ‘the proper procedure is to ask the district court whether it wishes to entertain the motion, or to grant it, and then move this court, if appropriate, for remand of the case.’ ” Scott v. Younger, 739 F.2d 1464, 1466 (9th Cir.1984) (quoting Long v. Bureau of Econ. Analysis, 646 F.2d 1310, 1318 (9th Cir.), vacated on other grounds, 454 U.S. 934, 102 S.Ct. 468, 70 L.Ed.2d 242 (1981)). Because Williams did not observe the procedure required to revest the district court with jurisdiction to consider his Rule 60(b) motion, we conclude that the district court’s December 17, 1999 order denying the motion is void for lack of jurisdiction. See Carriger, 971 F.2d at 332. We therefore vacate this order from which Williams appeals in No. 00-99001.

STANDARD OF REVIEW

We review de novo the district court’s denial of Williams’s habeas corpus petition. See Turner v. Calderon, 281 F.3d 851, 864 (9th Cir.2002). The district court’s partial grant of summary judgment in the state’s favor is reviewed de novo. See Clark v. City of Lakewood, 259 F.3d 996, 1003 (9th Cir.2001). Summary judgment is appropriate if, viewing the evidence in the light most favorable to Williams, the non-moving party, (1) the district court correctly applied the relevant substantive law, and (2) there are no genuine issues of material fact in dispute. See id. at 1004. Wé review for an abuse of discretion the district court’s denial of an evidentiary hearing and the scope of an evidentiary hearing held. Tapia v. Roe, 189 F.3d 1052, 1056 (9th Cir.1999); LaGrand v. Stewart, 133 F.3d 1253, 1270 (9th Cir.1998). The district court’s findings of fact are reviewed for clear error. Turner, 281 F.3d at 864. Pure questions of law and mixed questions of law and fact, such as whether Williams received ineffective assistance of counsel, are reviewed de novo. See Mayfield, 270 F.3d at 922.

Because Williams filed his habeas corpus petition before the AEDPA’s effective date, pre-AEDPA law applies to the merits of his petition. See id.; see also Slack, 529 U.S. at 481, 120 S.Ct. 1595. We presume that the state court’s factual findings are correct unless Williams “did not receive a full, fair, and adequate hearing in the State court proceeding.” 28 U.S.C. § 2254(d)(6) (West 1994); Silva v. Woodford, 279 F.3d 825, 835 (9th Cir.2002). Williams is entitled to a federal evidentiary hearing if (1) he has alleged facts that, if proven, would entitle him to habeas relief, and (2) he did not receive a full and fair opportunity to develop those facts in a state court. See Laboa v. Calderon, 224 F.3d 972, 981 n. 7 (9th Cir.2000); Phillips v. Woodford, 267 F.3d 966, 973 (9th Cir.2001). “Because of the limited scope of habeas corpus review, trial errors do not warrant relief unless the errors had substantial and injurious effect or influence in determining the jury’s verdict.” Turner, 281 F.3d at 864 (internal quotations omitted).

DISCUSSION

I. Guilt-Phase Challenges.

A. Excessive Security and Shackling at Trial. (Claim B)

Williams contends that he was unconstitutionally subjected to excessive security *587 and shackling at trial. We consider each claim in turn.

1. Excessive Security.

Williams argues that the district court erred in denying his excessive security claim on summary judgment, see Williams III, 48 F.Supp.2d at 996, because factual questions remained about the extent of the security measures taken at trial. Williams asks that we remand to the district court for an evidentiary hearing on his excessive security claim. 5

In his habeas corpus petition, Williams asserted that “the obvious presence of more than the usual number of deputy sheriffs” violated his constitutional right to a fair trial. See Holbrook v. Flynn, 475 U.S. 560, 568, 106 S.Ct. 1340, 89 L.Ed.2d 525 (1986) (noting that “certain [courtroom] practices pose such a threat to the ‘fairness of the factfinding process’ that they must be subjected to ‘close judicial scrutiny’”) (quoting Estelle v. Williams, 425 U.S. 501, 503-04, 96 S.Ct. 1691, 48 L.Ed.2d 126 (1976)); Morgan v. Aispuro, 946 F.2d 1462, 1464 (9th Cir.1991) (certain courtroom arrangements prejudice the presumption of innocence). To support this claim, Williams relies upon a declaration by an alternate juror and comments made by his counsel at trial. Sherry Wise-man, an alternate juror, averred that because her brother had been a marshal, she knew that there were normally two bailiffs or marshals in court during trials. She stated that during Williams’s trial, there were generally four marshals in the courtroom; one near Williams, one near the jury, and one on each side of the gate from the spectator section.

During trial, Joseph Ingber, Williams’s counsel, made the following comments to the jury:

I just happened to glance around ... and found out that there were eight, sometimes nine deputy sheriffs sitting in this courtroom. Some uniform, some non-uniform. In any event, the entire trial has been permeated with bailiffs sitting immediately behind Mr. Williams, behind me, over my shoulder. Everywhere I have turned, there have [sic] been the protective hand of the Los Angeles County Sheriff making sure of something. I’m not sure what.

Aside from Wiseman’s declaration and Ingber’s comments, Williams cites to no other evidence or factual allegation to support his excessive security claim.

*588 The noticeable deployment of security personnel in a courtroom during trial is not an inherently prejudicial practice that requires justification by an essential state interest specific to each trial. Holbrook 475 U.S. at 568-69, 106 S.Ct. 1340; Morgan, 946 F.2d at 1464. Rather, in light of the variety of ways that security guards can be deployed, courts must determine prejudice on a case-by-case basis. Holbrook 475 U.S. at 569, 106 S.Ct. 1340. In federal habeas corpus proceedings, federal courts reviewing the constitutionality of security personnel used at trial must “look at the scene presented to jurors and determine whether what they saw was so inherently prejudicial as to pose an unacceptable threat to defendant’s right to a fair trial; if the challenged practice is not found inherently prejudicial and if the defendant fails to show actual prejudice, the inquiry is over.” Id. at 572, 106 S.Ct. 1340; see also Ainsworth v. Calderon, 138 F.3d 787, 797 (9th Cir.1998).

The facts that Williams presents in his petition and through Wiseman’s declaration and Ingber’s trial comments do not permit a finding of actual prejudice. At most, only the assertion in Williams’s petition — that “the obvious presence of more than the usual number of deputy sheriffs” deprived him of a fair trial— supports an inference of actual prejudice. However, conclusory allegations by counsel that are unsworn and unsupported by any proof or offer of proof do not provide an adequate basis to obtain a federal evidentiary hearing. Phillips, 267 F.3d at 973; Coleman v. McCormick, 874 F.2d 1280, 1284-85 (9th Cir.1989) (en banc) (citing Frazier v. United States, 335 U.S. 497, 503, 69 S.Ct. 201, 93 L.Ed. 187 (1948)). Thus, we must determine whether Williams’s factual allegations support a conclusion that the deployment of security personnel at his trial was inherently prejudicial. The Supreme Court has said that security measures at trial are inherently prejudicial when they “tend[] to brand [the defendant] in [the jurors’] eyes with an unmistakable mark of guilt,” Holbrook, 475 U.S. at 571, 106 S.Ct. 1340 (internal quotations omitted), or when they create “an unacceptable risk ... of impermissible factors coming into play.” Id. at 570, 106 S.Ct. 1340 (quoting Williams, 425 U.S. at 505, 96 S.Ct. 1691); see also King v. Rowland, 977 F.2d 1354, 1358 (9th Cir.1992).

We hold that Williams’s factual allegations are insufficient to justify a conclusion that the scene presented to the jurors was inherently prejudicial. Wiseman’s declaration establishes only that she, an alternate juror, personally knew, due to her brother’s experience as a marshal, that four marshals reflected additional security precautions. She did not indicate that any juror shared this knowledge or impression at trial.

Moreover, the placement of the four marshals, as Wiseman described it, does not create an unacceptable risk that the jurors impermissibly inferred Williams’s guilt. As the Supreme Court has noted, “the presence of guards at a defendant’s trial need not be interpreted as a sign that he is particularly dangerous or culpable.... If they are placed at some distance from the accused, security officers may well be perceived more as elements of an impressive drama than as reminders of the defendant’s special status.” Holbrook, 475 U.S. at 569, 106 S.Ct. 1340. According to Wiseman, only one of the marshals was near Williams, with the others near the jury and the spectators. The jurors might “just as easily [have] believe[d] that the [marshals were] there to guard against disruptions emanating from outside the courtroom or to ensure that tense courtroom exchanges [did] not erupt into violence.” Id. (holding that the presence of *589 four uniformed state troopers did not unconstitutionally deprive the defendant of a fair trial); see also Ainsworth, 138 F.3d at 797 (the use of four, and sometimes six, deputy sheriffs did not violate the defendant’s right to a fair trial); King, 977 F.2d at 1358 (the use of three deputy sheriffs to guard the defendant was not improper).

Ingber’s comments regarding the placement of eight or nine deputy sheriffs, some of which were in uniform and some of which were not, also fail to support a conclusion of inherent prejudice, warranting a federal evidentiary hearing. As already discussed, counsel’s unsupported, unsworn, and conclusory allegations do not provide sufficient basis for an evidentiary hearing. Phillips, 267 F.3d at 973; Coleman, 874 F.2d at 1284-85.

Even assuming that Ingber’s comments could provide a basis for an evidentiary hearing, his comments do not compel a different conclusion than the one we have reached based upon Wiseman’s declaration because the comments do not necessarily present a different picture of Williams’s trial than Wiseman’s more specific account of the stations generally assumed by the four uniformed marshals. Although Ing-ber identified more security personnel than Wiseman, Ingber’s count includes an undisclosed number of plain-clothed security guards. When security personnel are in plain clothes, they are not easily identified by jurors as guards and thus do not create the same risk of impermissible juror inferences. See Holbrook, 475 U.S. at 568-70, 572, 106 S.Ct. 1340 (addressing the risk of prejudice from the conspicuous, or at least noticeable, deployment of identifiable guards in uniform, and expressing “a preference that officers providing courtroom security in federal courts not be easily identifiable by jurors as guards”). Because the eight or nine deputy sheriffs that Ingber identified include plain-clothed guards, the scene that Ingber portrays is not necessarily any more inherently prejudicial than Wiseman’s account of the four uniformed marshals at trial.

Any prejudice that Williams might have suffered from the presence of plain-clothed security guards at his trial cannot be attributed to inherently prejudicial courtroom procedures, but only to Ingber’s statements calling the jury’s attention to the guards’ presence. Williams, however, cannot rely upon any prejudice from his trial counsel’s statements implying extraordinary courtroom security measures to support his habeas claim that the security measures at trial impermissibly undermined the presumption of his innocence. See Morgan, 946 F.2d at 1465 (when defense counsel refused the opportunity to limit the implication that the security measures taken at trial were extraordinary, the petitioner could not use that decision to argue impermissible jury inferences).

We conclude that Williams has failed to allege facts that, if proven, would demonstrate that an excessive use of conspicuous security guards at his trial unconstitutionally deprived him of a fair trial. Accordingly, we decline Williams’s request that we order an evidentiary hearing on his excessive security claim. See Laboa, 224 F.3d at 981 n. 7. The district court properly granted the state’s motion for summary judgment on the claim.

2. Shackling.

Williams raises two arguments with respect to his shackling claim. First, he contends that the district court abused its discretion when it limited the scope of the evidentiary hearing on his shackling claim. He seeks remand to the district court for another hearing so that he can present additional oral testimony and cross-examine the state’s witnesses. Second, Williams asserts that the district *590 court’s factual findings are not supported by the record, and that based upon these erroneous factual findings, the district court improperly concluded that the physical restraints used at trial were harmless error. 6 See Williams IV, 41 F.Supp.2d at 1047-48.

(a) The Scope of the Evidentiary Hearing on Shackling.

In denying the state’s motion for summary judgment on Williams’s shackling claim, the district court stated that the “claim will be subject to the evidentiary hearing already scheduled in this case.” Williams III, 48 F.Supp.2d at 995. Subsequently, the parties submitted exhibits and direct witness testimony via written declarations on the shackling claim, and the district court ordered the parties to brief the question of whether the claim’s resolution required oral testimony in addition to the documents already in the record. After reviewing the record and the parties’ briefs, the district court decided that the record did not require further supplementation with oral testimony. One of Williams’s witnesses, however, refused to provide a written declaration. The distinct court allowed Williams to present oral testimony by this witness because it was not Williams’s fault that he could not secure the declaration.

Williams argues that the district court abused its discretion when it restricted the evidence presented on his shackling claim to written declarations, for the most part, and limited oral testimony. Williams claims that the district court, in resolving his claim mostly on a written record, deprived him of a full evidentiary hearing, of the opportunity to present facts, and of the opportunity to cross-examine the state’s witnesses.

We have previously held that a district court in a habeas corpus proceeding “need not conduct full evidentiary hearings,” but may instead “expand the record ... with discovery and documentary evidence." Watts v. United States, 841 F.2d 275, 277 (9th Cir.1988) (per curiam) (denying a habeas corpus petitioner’s contention that the district court erred in resolving a claim based on contradictory affidavits and interrogatories without an evidentiary hearing at which oral testimony could be provided). We stated that “[decisions to hold hearings and conduct discovery in [habeas corpus] cases are committed to the [district] court’s discretion.” Id. The district court must only “give the prisoner’s claim ‘careful consideration and plenary processing, including full opportunity for presentation of the relevant facts.’ ” Id. (quoting Blackledge v. Allison, 431 U.S. 63, 82-83, 97 S.Ct. 1621, 52 L.Ed.2d 136 (1977)).

Other circuits have similarly held that “there is a permissible intermediate step that may avoid the necessity of an expensive and time consuming hearing in every [habeas corpus] case. It may instead be *591 perfectly appropriate, depending upon the nature of the allegations, for the district court to proceed by requiring that the record be expanded to include letters, documentary evidence, and, in an appropriate case, even affidavits.” Chang v. United States, 250 F.3d 79, 86 (2nd Cir.2001) (finding no abuse of discretion when the district court dismissed the petitioner’s claim without an evidentiary hearing with live witnesses) (citing Raines v. United States, 423 F.2d 526, 529-30 (4th Cir.1970)); see also Blackledge, 431 U.S. at 81-82, 97 S.Ct. 1621 (“[A]s is now expressly provided in the Rules Governing Habeas Corpus Cases, the district judge ... may employ a variety of measures in an effort to avoid the need for an evidentiary hearing.... In short, it may turn out ... that a full evidentiary hearing is not required.”); Spreitzer v. Peters, 114 F.3d 1435, 1456 (7th Cir.1997) (same). In light of this case law, we conclude that it was within the district court’s discretion to choose a middle path allowing the parties to present evidence through written declarations and limited oral testimony.

Williams, however, contends that the district court’s denial of a full evidentiary hearing was an abuse of discretion because his cross-examination of the state’s witnesses might have brought out defects in their written affidavits. Williams cites the Supreme Court’s statement in Blackledge that “[w]hen the issue is one of credibility, resolution on the basis of affidavits can rarely be conclusive.” Blackledge, 431 U.S. at 82 n. 25, 97 S.Ct. 1621 (internal quotations omitted). However, in construing Blackledge, our circuit and the Second Circuit have found no abuse of discretion when the district court “conclude[d] that [a full evidentiary] hearing would not offer any reasonable chance of altering its view of the facts.” Chang, 250 F.3d at 86; Watts, 841 F.2d at 277 (finding that, in the case at hand, the issue of credibility could be conclusively decided on the basis of documentary testimony and evidence in the record). Such was the case here: the district court reviewed the declarations and exhibits already present in the record, considered the parties’ arguments regarding the need for oral testimony and cross-examination, and concluded that this evidence would not alter the court’s view of the record. The district court did not abuse its discretion in determining that oral testimony and cross-examination were not necessary because the documentary evidence submitted fully presented the relevant facts of Williams’s shackling claim.

(b) The Merits of Williams’s Shackling Claim.

A criminal defendant has a constitutional right to be free of shackles and handcuffs in the presence of the jury absent an essential state interest that justifies the physical restraints. Ghent v. Woodford, 279 F.3d 1121, 1132 (9th Cir.2002); Rhoden v. Rowland, 172 F.3d 633, 636 (9th Cir.1999). A claim of unconstitutional shackling is susceptible to harmless-error analysis, however. Duckett v. Godinez, 67 F.3d 734, 749 (9th Cir.1995); Castillo v. Stainer, 983 F.2d 145, 148 (9th Cir.1992), amended by 997 F.2d 669 (9th Cir.1993). An “ unjustified decision to restrain a defendant at trial requires reversal only if the shackles or handcuffs had “substantial and injurious effect or influence in determining the jury’s verdict.” Castillo, 997 F.2d at 669 (quoting Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)).

After conducting an evidentiary hearing on Williams’s claim that his physical restraints at trial violated his right to due process, the district court denied the claim on the ground that the use of restraints was harmless error. See Williams IV, 41 F.Supp.2d at 1047-48. The district court *592 based its decision on the following factual findings. Although a chain restrained Williams’s legs during trial, no member of the jury saw the leg chain. Williams’s hands were free of restraints during trial. However, on one occasion, a juror observed Williams in handcuffs with a coat draped over his handcuffed hands as he was being taken to or from the courtroom. No other juror saw Williams in handcuffs. See id. Williams challenges these factual findings underlying the district court’s denial of his claim.

“Where there are two permissible views of the evidence, the factfinder’s choice between them cannot be clearly erroneous.” Anderson v. Bessemer City, 470 U.S. 564, 574, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). We give “due regard” to the district court’s opportunity to judge the credibility of witnesses, see Fed.R.Civ.P. 52(a), and we will disturb the district court’s credibility determinations or factual findings only when, “on the entire evidence,” we are “left with the definite and firm conviction that a mistake has been committed.” Easley v. Cromartie, 532 U.S. 234, 242, 121 S.Ct. 1452, 149 L.Ed.2d 430 (2001) (internal quotations omitted).

After reviewing the record, we conclude that none of the district court’s factual findings are clearly erroneous. Thé bailiff to the trial judge provided detailed testimony about a thin, metal leg chain on Williams’s ankles as he sat in court during trial. No juror indicated that Williams’s legs were in restraints, however, and the bailiff stated that the jury was not able to view Williams’s leg chain or feet under the defense table at trial. ■ The bailiff also testified that Williams was brought into the courtroom and sat down at the defense table before the jury was allowed to enter, ■ and that Williams was not allowed to stand until after the jury ■left. The penalty-phase jury foreman- confirmed this procedure. Given this record, the district court did not clearly err in concluding that Williams’s leg chain was not visible to the jury.

There also is no clear error in the district court’s finding that Williams’s hands were free of restraints in the courtroom. Williams disputes this factual finding, relying upon Juror Kellick’s declaration in which she claimed to have seen Williams in handcuffs throughout the entire trial. The district court did not clearly err in disbelieving this declaration given that Juror Kellick averred in a later declaration that she had “vivid memories” of seeing Williams without handcuffs “lots of times,” and particularly remembered him writing on a yellow pad. No other juror indicated observing Williams in handcuffs in the courtroom, and the bailiff testified that Williams was not handcuffed at any point in front of the jury.

One juror, however, testified that he recalled seeing Williams with his hands together, as though in handcuffs, and a coat draped over his likely handcuffed hands. The juror stated that he never actually saw the handcuffs around Williams’s wrists, but inferred their existence based upon how Williams was holding his hands. In light of this testimony and the other evidence in the record, the district court did not clearly err in finding that the juror must have seen Williams in handcuffs as he was being brought to or from the courtroom.

Even if we assume that Williams’s physical restraints at trial were unjustified, we conclude that the district court properly held that the error was harmless. When the jury never saw the defendant’s shackles in the courtroom, we have held that the shackles did not prejudice the defendant’s right to a fair trial. See Castillo, 997 F.2d at 669 (a waist chain that *593 could not be seen by the jury was harmless error); Packer v. Hill, 291 F.3d 569, 583 (9th Cir.2002) (no prejudice resulted from the defendant’s leg brace when no juror interviewed after trial remembered seeing a leg brace on the defendant); Rich v. Calderon, 187 F.3d 1064, 1069 (9th Cir.1999) (no prejudice when the ankle chains used at trial were not visible to the jury due to a curtain draped around the defense table); United States v. Collins, 109 F.3d 1413, 1418 (9th Cir.1997) (the defendant’s leg shackles were harmless error because a curtain around the defense table hid the shackles from the jury’s view). Thus, the use of the leg chain at Williams’s trial was harmless error.

We have also held that a jury’s brief or inadvertent glimpse of a defendant in physical restraints outside of the courtroom does not warrant habeas relief unless the petitioner makes an affirmative showing of prejudice. See Ghent, 279 F.3d at 1133 (the jurors’ occasional, brief glimpses of the defendant in handcuffs and other restraints in the hallway at the entrance to the courtroom was not prejudicial); United States v. Olano, 62 F.3d 1180, 1190 (9th Cir.1995) (“a jury’s brief or inadvertent glimpse of a defendant in physical restraints is not inherently or presumptively prejudicial to a defendant”); Castillo, 983 F.2d at 148 (no prejudice when, during transport to or from the courtroom, some members of the jury pool saw the defendant in shackles in the court corridor); United States v. Halliburton, 870 F.2d 557, 560-62 (9th Cir.1989) (jurors’ inadvertent observation of the defendant in handcuffs in the corridor did not prejudicially impair the defendant’s right to a fair trial); Wilson v. McCarthy, 770 F.2d 1482, 1485-86 (9th Cir.1985) (the jury’s brief viewing of defendant’s shackles as he left the witness stand at the conclusion of his testimony was not prejudicial). Accordingly, the juror’s viewing of Williams in handcuffs with a coat draped over his handcuffed hands as he went to or from the courtroom was not inherently or presumptively prejudicial. Williams has made no showing of actual prejudice from this sighting, and as the district court noted, the fact that a coat covered Williams’s handcuffs minimized any possible prejudice. See Williams IV, 41 F.Supp.2d at 1048. We therefore affirm the district court’s denial of Williams’s claim of unconstitutional shackling.

B. Samuel Coleman’s Coerced Testimony. (Claim E)

Williams argues that the trial court’s improper admission of Samuel Coleman’s coerced testimony violated Williams’s constitutional right to due process. Although Williams lacks standing to complain about infringements of Coleman’s constitutional rights, see Rakas v. Illinois, 439 U.S. 128, 139-40, 99 S.Ct. 421, 58 L.Ed.2d 387 (1978), Williams is entitled to habeas relief if the trial court’s admission of Coleman’s testimony rendered the trial so fundamentally unfair as to violate due process. See Karis v. Calderon, 283 F.3d 1117, 1129 n. 5 (9th Cir.2002); Jeffries v. Blodgett, 988 F.2d 923, 934-35 (9th Cir.1993).

At trial, Coleman testified that Williams admitted to robbing and killing people on Vermont Street, which is where the Brook-haven Motel was located. Coleman also testified that Williams said that he had obtained approximately $50 from the robbery-murder, with which he planned to buy PCP. In a sworn declaration, subsequently presented in Williams’s habeas corpus proceedings, Coleman attested to the following events. Williams and Coleman were driving in Coleman’s car when the police stopped and arrested them both in 1979. At the city jail, police officers beat Coleman and then interrogated him, accus *594 ing him of having committed murder. In Coleman’s words, “[t]he beating put so much fear into- me — I was so terrorized and in so much pain physically — that I told the police just what they wanted to hear about Stanley.” Then someone from the district attorney’s office visited Coleman and informed him that the state would give him immunity if he testified against Williams. Coleman agreed because he feared further beatings and being charged with murder. The police arrested Coleman again in 1980 on an unrelated drug charge and said that he would get jail time on the charge if he did not testify against Williams. Coleman subsequently received a diversion sentence on the charge.

The district court correctly relied upon United States v. Mattison, 437 F.2d 84 (9th Cir.1970) (per curiam), in denying Williams’s due process claim regarding Coleman’s testimony. See Williams III, 48 F.Supp.2d at 1001. In Mattison, the appellant argued that a government witness’s trial testimony was involuntary because the government had unconstitutionally interrogated the witness and created financial incentives for the witness to testify. Mattison, 437 F.2d at 85. Like Williams, the appellant contended that the trial court’s admission of the involuntary testimony violated his right to due process. See id. In Mattison, we concluded, however, that the appellant’s evidence of coercive interrogation and inducement to testify was insufficient to show that the witness’s trial testimony was involuntary. We stressed that “[b]y the time of trial, the psychologically coercive atmosphere of that interrogation must surely have dissipated. There [was] no indication that [the witness] was told at any time by anyone what he should say on the witness stand.” Id. We also noted that the witness was subject to cross-examination, through which the appellant brought out the facts of the interrogation and the inducement to testify, and that the jury was free to observe the witness’s demeanor and gauge his credibility. Id. Because the alleged •facts of coercive interrogation and inducement to testify did not support a conclusion that the witness’s trial testimony was involuntary; we denied the appellant’s due process claim. See id.

Williams’s claim that Coleman’s testimony at trial was involuntary depends upon (1) evidence that the police used illegal, coercive measures to interrogate him in 1979, and (2) evidence that the police induced him to testify in exchange for immunity in Williams’s case and sentencing leniency on the 1980 drug charge. Williams does not allege that the prosecution introduced at trial any of Coleman’s statements that were illegally obtained at Coleman’s 1979 interrogation. Williams also does not claim that the state employed coercive tactics at the time of trial or immediately before trial in order to secure Coleman’s trial testimony. Thus, as in Mattison, the question before us is whether the post-arrest coercion of a government witness so tainted that witness’s trial testimony as to render the testimony’s admission a violation of the defendant’s right to due process.

An interrogating agent’s suggestion that a suspect’s cooperation with the government will have a positive effect on the suspect’s possible sentence is not an improper inducement that causes the suspect’s later testimony for the government to be involuntary. United States v. Leon Guerrero, 847 F.2d 1363, 1366 (9th Cir.1988); see also United States v. Moody, 778 F.2d 1380, 1384-85 (9th Cir.1985) (witness testimony provided pursuant to a plea agreement was not involuntary or coerced). Consequently, the statement by the police to Coleman, implying that Coleman would not receive jail time on his 1980 *595 drug charge so long as he testified against Williams, did not render involuntary Coleman’s trial testimony against Williams.

However, a promise of leniency accompanied by threats or other coercive practices constitutes improper influence and makes a subsequent inculpatory statement involuntary. See United States v. Tingle, 658 F.2d 1382, 1336 (9th Cir.1981) (the defendant’s confession was involuntary when it was induced by an interrogating officer who accused the defendant of lying, recited the maximum penalties of crimes that could be charged, threatened the defendant that she might not see her two-year-old child if she went to prison, and promised the defendant that the agent would inform the prosecutor if she cooperated or refused to cooperate). Assuming the truth of Coleman’s declaration, then the beatings, threatened murder charge, and offer of immunity in exchange for Coleman’s testimony against Williams were coercive and rendered involuntary Coleman’s statements incriminating Williams at the 1979 interrogation. See Leon Guerrero, 847 F.2d at 1366 (in assessing the voluntariness of an inculpatory statement, we must decide “whether, considering the totality of the circumstances, the government obtained the statement by physical or psychological coercion or by improper inducement so that the suspect’s will was overborne”).

In resolving whether the officers’ coercion of Coleman at the 1979 interrogation so tainted his trial testimony as to render it involuntary, “[w]e must determine “whether, granting establishment of the primary illegality, the evidence to which ... objection is made has been come at by exploitation of that illegality or instead by means sufficiently distinguishable to be purged of the primary taint.’ ” Collazo v. Estelle, 940 F.2d 411, 421 (9th Cir.1991) (en banc) (quoting Maguire, Evidence of Guilt 221 (1959)). We look at factors like the passage of time between Coleman’s illegal interrogation and his trial testimony, and whether intervening circumstances sufficiently insulated his testimony from the effect of the prior coercion. See Collazo, 940 F.2d at 421; Brown v. Illinois, 422 U.S. 590, 603-04, 95 S.Ct. 2254, 45 L.Ed.2d 416 (1975).

Applying these factors, we agree with the district court that Coleman’s trial testimony was sufficiently voluntary. By the time Coleman testified at trial in 1981, approximately two years had passed since his illegal interrogation in 1979. With this passage of time, the physically and psychologically coercive atmosphere of the interrogation had certainly dissipated. See Mattison, 437 F.2d at 85 (the coercion of the witness’s illegal post-arrest interrogation had dissipated by the time of trial); see also United States v. Lewis, 833 F.2d 1380, 1387-88 (9th Cir.1987) (any illegality in the first interrogation of the defendant following surgery did not taint her confession given 24 hours later). In addition, by the time of trial, Coleman was represented by counsel, who had negotiated Coleman’s grant of immunity in Williams’s case in exchange for Coleman’s testimony against Williams. 7 “With a lawyer present the likelihood that the police will practice coercion is reduced, and if coercion is nevertheless exercised the lawyer can testify to it in court.” Cooper v. Dupnik, 963 F.2d 1220, 1240 (9th Cir.1992) (en banc). The record does not indicate that Coleman’s attorney objected to coercive practices by *596 the state at trial or in the negotiations regarding Coleman’s immunity.

There is also no evidence that the admission of Coleman’s trial testimony deprived Williams of a fair trial in violation of due process. Williams does not allege that Coleman’s trial testimony was false, or-that the state at any time instructed Coleman in how to inculpate Williams or in what to say on the witness stand. See Mattison, 437 F.2d at 85 (no evidence suggested that the government had coached the witness regarding his testimony). Williams did not lack the opportunity at trial to test the voluntariness and veracity of Coleman’s testimony through cross-examination. According to Coleman’s declaration, Williams knew that the police had beaten Coleman at-the city jail. Thus, defense counsel might have cross-examined Coleman about the coercive police tactics employed at his 1979 interrogation. Coleman did disclose at trial the grant of immunity that he had received in exchange for his trial testimony, and defense counsel questioned him on the subject. The jury was therefore free to draw inferences regarding Coleman’s credibility and motivations for testifying from the fact that he had entered into .this bargain with the state. See id. (there was no violation of due process when the witness, who was previously illegally interrogated, was subject to cross-examination at trial through which the jury could assess the witness’s credibility); Moody, 778 F.2d at 1384-85 (rejecting the argument that witness testimony pursuant to a plea agreement is so unreliable as to violate due process by pointing out that the witness’s motivation for testifying can be explored through cross-examination). Finally,.the fact that Coleman had counsel at Williams’s trial provided some safeguard for the truth of Coleman’s trial testimony. “The presence of a lawyer can ... help to guarantee that ... a fully accurate statement [is given] to the police and that the statement is rightly reported by the prosecution at trial.” Cooper, 963 F.2d at 1240.

Because Williams’s argument regarding Coleman’s trial testimony is essentially indistinguishable from that raised in Matti-son, our decision in that case compels us to deny Williams’s claim. Williams has not alleged sufficient facts to demonstrate that Coleman’s trial testimony was involuntary and that its admission rendered Williams’s trial so fundamentally unfair as to violate due process. We affirm the district court’s grant of summary judgment on this claim. 8

C. The Prosecution’s Suppression of Material Evidence Favorable to the Defense. (Claims F & I)

Williams argues that the prosecution’s failure to disclose material evidence impeaching the credibility of two key government witnesses violated his right to due process. In particular, Williams claims that the prosecution suppressed, and failed to correct false testimony regarding, a deal whereby the state procured the testimony of James Garrett in exchange for leniency in sentencing in an unrelated criminal case pending against Garrett. 9 Williams also *597 contends that the prosecution did not turn over two tapes in its possession that undermined the veracity of George Oglesby’s testimony inculpating Williams. Williams asserts that the district court erred in granting the state’s summary judgment motion on these claims, see Williams III, 48 F.Supp.2d at 1002-03, 1011-13, and requests remand for an evidentiary hearing on them.

Due process requires that the prosecution disclose to the defense evidence that is both favorable to the accused and material to guilt or punishment. United States v. Agurs, 427 U.S. 97, 107, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976); Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). The prosecution must turn over evidence impeaching its witnesses, Silva, 279 F.3d at 854; United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985), and also correct false testimony by its witnesses. Phillips, 267 F.3d at 984-85; California v. Trombetta, 467 U.S. 479, 485, 104 S.Ct. 2528, 81 L.Ed.2d 413 (1984). Evidence is material when there is “a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have , been different. A ‘reasonable probability’ is a probability sufficient to undermine confidence in the outcome.” Bagley 473 U.S. at 682, 105 S.Ct. 3375; see also Karis, 283 F.3d at 1128.

1. The Undisclosed Deal with James Garrett. (Claim F)

The prosecution must disclose to the defense a government agreement with a witness that may motivate the witness to testify and that may affect the outcome of trial. Giglio v. United States, 405 U.S. 150, 154-55, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). To prevail on his claim, Williams must first demonstrate the existence of an agreement whereby the state offered James Garrett leniency in sentencing in the criminal case pending against him in exchange for his testimony against Williams. See Williams v. Calderon, 52 F.3d 1465, 1475 (9th Cir.1995) (denying the petitioner’s claim that the prosecution failed to disclose a deal with a testifying witness when the petitioner could not show the existence of the alleged deal).

The facts and circumstances that Williams alleges show only that James Garrett testified against Williams in the hope that his testimony would result in a reduced sentence in the criminal case against him. Williams’s factual allegations are not sufficient to entitle him to habeas corpus relief because they do not establish the existence of the asserted agreement between the state and Garrett. See Williams, 52 F.3d at 1474-75 (no due process violation for failure to disclose an agreement with a testifying witness when the prosecution made no promises, and only suggested that the witness might receive a reduced penalty if he testified); Alderman v. Zant, 22 F.3d 1541, 1555 (11th Cir.1994) (“The simple belief by a defense attorney that his client may be in a better position to negotiate a reduced penalty should he testify ... is not an agreement within the purview of Giglio.”). Accordingly, we do not remand for an evidentiary hearing because the district court properly granted summary judgment on Williams’s claim that the state unconsti *598 tutionally suppressed its deal with James Garrett. See Laboa, 224 F.3d at 981 n. 7 (a federal evidentiary hearing requires the allegation of facts that, if proven, would warrant relief).

2. The Suppressed Tape Recordings. (Claim I)

The prosecution has a duty to turn over to the defense all exculpatory evidence material to guilt or punishment, including evidence affecting the credibility of witnesses whose testimony may be determinative of the trial outcome. Giglio, 405 U.S. at 154, 92 S.Ct. 763. Williams argues that the prosecution violated its duty by suppressing two tape recordings, one made in 1978 and the other in 1979, that undermine the credibility of Oglesby’s trial testimony. Williams contends that the 1978 tape recording of a telephone conversation between Oglesby and prison inmate Leslie White shows them conspiring to fabricate testimony in an unrelated murder case. However, the California Supreme Court found otherwise.

After an evidentiary hearing conducted in conjunction with Williams’s third state habeas corpus petition, the referee appointed by the California Supreme Court found that Lieutenant Fitzgerald, a member of the Los Angeles Sheriffs Office, made the 1978 tape recording at the request of Oglesby, who did not want to become entangled in White’s purported scheme to escape from jail. Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1080. White’s scheme was to implicate Oglesby in a crime in Ventura so that White, who was in custody in Los Angeles, could be transferred to Ventura to testify against Oglesby and attempt to escape from the Ventura jail. Id. Adopting these factual findings by the referee, the California Supreme Court declared that the 1978 tape recording “showed merely that Oglesby contacted Fitzgerald to secure his help when Oglesby thought that he was going to be ‘used’ by, and falsely implicated by, Leslie White.” Id. at 1079. Because we must defer to the California Supreme Court’s factual findings on the 1978 tape recording, see 28 U.S.C. § 2254(d) (West 1994), 10 we conclude that the recording is not exculpatory evidence that impeaches Oglesby’s credibility. See Giglio, 405 U.S. at 154, 92 S.Ct. 763. Accordingly, the prosecution’s failure to disclose the 1978 tape recording to the defense did not violate due process.

Williams also alleges that the prosecution improperly suppressed a 1979 tape recording of an interview between White and investigators for the Los Angeles district attorney’s office, in which White asserts that Oglesby committed perjury when he testified in another, unrelated criminal case. Even assuming that this tape recording is the exculpatory impeachment evidence that Williams claims it to be, 11 the recording is not material to Williams’s guilt or punishment. See Bagley, 473 U.S. at 682, 105 S.Ct. 3375. Had the defense used the 1979 tape recording *599 to undermine Oglesby’s credibility, this evidence would have been merely- cumulative of other evidence that the defense presented to impeach Oglesby. At trial, the defense effectively called into question the truthfulness of Oglesby’s- testimony through cross-examination. The defense elicited from Oglesby testimony showing, inter alia, that (1) he was an admitted murderer and accused rapist, (2) his plea agreement with the state drastically reduced his possible sentence on the charges against him, (3) he believed that his prior testimony for the state in an unrelated murder case would benefit him at sentencing, (4) he hoped to benefit further from his testimony against Williams, (5) he was a reputed “snitch,” and (6) other inmates fed him fabricated information so that he would go to the authorities with it. In light of this evidence presented, the district court correctly determined that the 1979 tape recording “would not have cast [Oglesby] in a significantly worse light.” Williams III, 48 F.Supp.2d at 1013. Because there exists no “reasonable probability that, had [the 1979 tape recording] been disclosed to the defense, the result of the proceedings would have been different,” Bagley, 473 U.S. at 682, 105 S.Ct. 3375, we decline to remand for an eviden-tiary hearing, see Laboa, 224 F.3d at 981 n. 7, and affirm the district court’s denial of this claim on summary judgment.

D. Improper Admission of Testimony of Government Agent George Oglesby. (Claims G & H)

In his state post-conviction proceedings, Williams argued that the trial court’s admission of Oglesby’s testimony violated the Sixth Amendment right to counsel because Oglesby was a government agent who deliberately elicited incriminating information from Williams in contravention of United States v. Henry, 447 U.S. 264, 100 S.Ct. 2183, 65 L.Ed.2d 115 (1980), and Massiah v. United States, 377 U.S. 201, 84 S.Ct. 1199, 12 L.Ed.2d 246 (1964). After two state evidentiary hearings on this claim, the California Supreme Court found that Oglesby did not act as a government agent prior to May 21, 1979, when Oglesby first informed law enforcement authorities about Williams’s confession of criminal conduct and escape plans. The California Supreme Court then concluded that any impropriety in admitting evidence that Oglesby obtained from Williams after May 21, 1979 was harmless error because this post-May 21,1979 evidence was cumulative of the evidence lawfully acquired before May 21, 1979. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1087-88. The district court denied this claim on summary judgment, deferring to the California Supreme Court’s factual findings and affirming its harmless-error analysis. See Williams III, 48 F.Supp.2d at 1003-11.

On appeal, Williams argues only that the two state evidentiary hearings on the factual issue of Oglesby’s status as a government agent were not full and fair, and that the district court therefore improperly deferred to the California Supreme Court’s factual findings. Under pre-AEDPA § 2254(d), we presume that the California Supreme Court’s factual determinations are correct unless Williams demonstrates that he “did not receive a full, fair, and adequate hearing in the State court proceeding.” 28 U.S.C. § 2254(d)(6) (West 1994); Silva, 279 F.3d at 835. Williams claims that the state hearings were not full and fair because (1) the prosecution suppressed material, exculpatory evidence at the first hearing, and (2) the prosecution and the state referee conducting the hearings refused to grant Williams’s witnesses use immunity to testify at the second hearing, and these witnesses declined to testify, invoking their Fifth Amendment rights against self-incrimination.

*600 Williams’s first argument is without merit because at the second state hearing he presented the evidence that he claims the prosecution improperly suppressed. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1078. The second hearing therefore cured any inadequacy of the first due to the unavailability of the evidence that Williams identifies. Thus, we cannot conclude that any failure by the prosecution to disclose this evidence denied Williams a full, fair, and adequate hearing in state court. See 28 U.S.C. § 2254(d)(6) (West 1994).

With respect to Williams’s second argument, we note that the prosecution’s refusal to grant use immunity to a defense witness denies the defendant a fair trial only when (1) the witness’s testimony would have been relevant, and (2) the prosecution refused to grant the witness use immunity with the deliberate intention of distorting the fact-finding process. See United States v. Westerdahl, 945 F.2d 1083, 1086 (9th Cir.1991); United States v. Lord, 711 F.2d 887, 891 (9th Cir.1983). To demonstrate the prosecutorial misconduct of the second prong, Williams must show that the prosecution intentionally caused a defense witness to invoke the Fifth Amendment right against self-incrimination, or that the prosecution granted immunity to a government witness in order to obtain that witness’s testimony, but denied immunity to a defense witness whose testimony would have directly contradicted that of the government witness. See United States v. Duran, 189 F.3d 1071, 1087 (9th Cir.1999). We apply this due process standard to determine whether Williams was denied a full, fair, and adequate hearing in state court under pre-AEDPA § 2254(d)(6). We will assume that Williams satisfies the “minimal requirement” that his witnesses’ testimony would have been relevant to his Sixth Amendment claim. See United States v. Whitehead, 200 F.3d 634, 640 (9th Cir.2000) (“To satisfy the relevance prong, a defendant need not show that the testimony sought was either clearly exculpatory or essential to the defense; the testimony need be only relevant.”) (internal quotations omitted). In the proceedings before the California Supreme Court, Williams argued that Leslie White would have provided testimony consistent with White’s statements on the 1979 tape recording 12 and in a 1989 declaration. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1090 n. 17. On the 1979 tape recording, White asserted that the Los Angeles police and district attorney’s office engaged in illegal tactics to bolster weak prosecution cases. According to White, certain members of the police department and district attorney’s office placed jail-house informants, like White and Oglesby, in cells near a defendant’s cell and encouraged them to obtain incriminating information from the defendant. If the defendant did not make any inculpatory statements, White alleged that the police officers or prosecutors forced the jailhouse informants to fabricate a confession of criminal conduct by the defendant. In the 1989 declaration, White claimed that Oglesby, at the behest of the police, fabricated his testimony regarding Williams’s admission of responsibility for the Brookhaven Motel murders and robbery and regarding Williams’s escape plans. Before the California Supreme Court, Williams also contended that witnesses Ferril Mickens, Larry Montez, and Steven Cisneros would have testified generally about jailhouse- *601 informant practices and specifically about Oglesby’s practices. See id. at 1092 n. 20. Assuming that Williams’s witnesses would have testified as he claimed in state court, 13 the witnesses’ testimony would have been relevant to the factual question of whether and when Oglesby acted as a government agent and deliberately elicited incriminating statements from Williams.

Turning to the prosecutorial misconduct required under the second prong, we note that Williams does not contend that the prosecution granted immunity to its witnesses, while denying immunity to his witnesses, and nothing in the record supports an argument that the prosecution attempted to distort the fact-finding process in this manner. Thus, resolution of the second prong turns on whether the prosecution took affirmative steps to prevent Williams’s witnesses from testifying. In deciding this matter, we rely upon the California Supreme Court’s factual findings, which Williams does not contest, regarding his witnesses’ refusals to testify. See 28 U.S.C. § 2254(d) (West 1994).

Two days before the rescheduled eviden-tiary hearing was set to begin, Leslie White was indicted and arrested for providing perjured testimony in past cases. One week later, after Williams called White as a witness, White asserted -his Fifth Amendment right against self-incrimination and declined to testify. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1090-91. When called to the stand, Ferril Mickens, Larry Montez, and Steven 'Cisne-ros also invoked their Fifth Amendment rights against self-incrimination and refused to testify. Williams’s counsel had subpoenaed these three witnesses, but failed to secure protective orders for their transportation and housing during the evi-dentiary hearing. Mickens did not testify primarily because Williams and his counsel intimidated Mickens. Mickens feared that his testimony might result in bodily harm to himself or his family members. Montez declined to testify because he believed that his testimony would incriminate him and felt intimidated by Williams. Cisneros invoked his Fifth Amendment right for two reasons. First, given White’s indictment, Cisneros feared that he might be indicted for perjury if he provided testimony helpful -to Williams. Second, Cisneros feared for his safety during' transportation and housing in the Los Angeles County jail system.- See id. at 1092-93.

Based upon these factual findings and other evidence in the record, we conclude that the prosecution did not improperly cause Williams’s witnesses to invoke . their Fifth Amendment rights against self-incrimination. Undue prosecutorial interference in a defense witness’s decision to 'testify arises when the prosecution intimidates or harasses the witness to discourage ■ the witness from testifying, for example, by threatening the witness with prosecution for perjury or *602 other offenses. United States v. Angiulo, 897 F.2d 1169, 1192 (1st Cir.1990); see also United States v. Morrison, 535 F.2d 223, 229 (3d Cir.1976) (the prosecutor’s repeated statements to the defense witness about the dangers of perjury and self-incrimination and about the witness’s right not to testify, culminating in a highly intimidating personal interview, improperly interfered with the witness’s choice to testify and violated the defendant’s right to due process); Lord, 711 F.2d at 891 (remanding for an evidentiary hearing on whether the prosecutor engaged in misconduct when the prosecutor told the defense witness about the self-incrimination privilege, said that the government would not prosecute the witness if he submitted to an interview and testified truthfully, and stated that any prosecution of the witness depended upon his testimony). The prosecution’s conduct must amount to a substantial interference with the defense witness’s free and unhampered determination to testify before the conduct violates the defendant’s right to due process. United States v. Emuegbunam, 268 F.3d 377, 400 (6th Cir.2001); United States v. Pinto, 850 F.2d 927, 932 (2d Cir.1988).

No prosecutorial misconduct tainted White’s decision not to testify at the second state hearing. The record does not support a conclusion that the prosecution brought baseless perjury charges against White to harass him and discourage him from testifying at the hearing. To the contrary, the record suggests that the charges were well-founded given White’s admissions to the authorities that he had provided perjured testimony on a number of occasions. Moreover, the prosecution does not abuse its discretion when it refuses to grant use immunity to a defense witness who has been indicted or is the subject of a criminal investigation. See United States v. Croft, 124 F.3d 1109, 1117 (9th Cir.1997) (“declin[ing] to adopt a rule that would require the government to grant transactional immunity to an indicted co-conspirator, or to a more marginal witness indicted on related charges”); United States v. Condo, 741 F.2d 238, 239 (9th Cir.1984) (the denial of immunity for defense witnesses that were themselves the target of prosecutorial investigation did not deprive the defendant of a fair trial); accord Emuegbunam, 268 F.3d at 401; United States v. Cohen, 171 F.3d 796, 802 (3d Cir.1999); United States v. Mitchell, 886 F.2d 667, 669-670 (4th Cir.1989); United States v. Hooks, 848 F.2d 785, 802 (7th Cir.1988); United States v. Drape, 668 F.2d 22, 26 (1st Cir.1982). “While a grant of use immunity theoretically does not improve the legal position of the person immunized, in that he still can be prosecuted for his crime, in practice the burden placed on the government to prove that any evidence obtained against the immunized subject is not tainted by the suspect’s statement can significantly impair future prosecutions.” United States v. Thevis, 665 F.2d 616, 640 (5th Cir.1982). Williams sought White’s testimony on how White, Oglesby, and other jail-house informants fabricated testimony in criminal cases, the very subject of the perjury charges against White. Thus, the prosecution’s refusal to grant White use immunity that could have jeopardized the state’s case against White was not misconduct that rendered the state evidentiary hearing unfair.

We also find no indication that the prosecution improperly interfered in a decision by Mickens, Montez, or Cisneros to testify at the state hearing. Williams points to no direct communication between the prosecution and these witnesses on any subject. Compare Morrison, 535 F.2d at 229 (communication between the prosecu *603 tor and defense witness discouraged the witness from testifying); Lord, 711 F.2d at 891 (similar prosecutor-witness communication). Moreover, to the extent that White’s perjury indictment influenced these witnesses to invoke their Fifth Amendment rights against self-incrimination, this influence does not amount to prosecutorial misconduct. As already noted, the record does not indicate that White’s perjury charges were baseless or pursued with the intent to intimidate or stifle the testimony of Williams’s -witnesses. Even if we assume that White’s indictment was a warning to these witnesses, “merely warning a. witness of the consequences of perjury” does not unduly pressure the witness’s choice to testify or violate the defendant’s right to due process. Emuegbunam, 268 F.3d at 400 (no prosecutorial interference with the defense witness’s decision not to testify when his concern about his exposure to potential criminal liability motivated the decision, not any threats by government officials); Hooks, 848 F.2d at 799-802 (noting that “[i]t is not improper per se for a ... prosecuting attorney to advise prospective witnesses of the penalties for testifying falsely,” and finding no prosecutorial misconduct when the prosecutor simply informed the court and counsel for the defense witnesses that the witnesses could be prosecuted if they testified falsely, and there was no evidence of threats and intimidation).

Williams fails to show that the prosecution denied his witnesses use immunity with the deliberate intention of distorting the fact-finding process. Because Williams does not establish that the second state evidentiary hearing on his Sixth Amendment claim was not full and fair-, the district court properly deferred under pre-AEDPA § 2254(d) to the California Supreme Court’s factual determinations with respect to this claim. Accordingly, we decline Williams’s request for remand for an evidentiary hearing. 14

E. Incompetence To Stand Trial. (Claim A)

Williams claims violations to his due process rights because the trial judge failed sug sponte to conduct a competency hearing, and because he was tried while incompetent. We consider each claim in turn. 15

1. Procedural-Due-Process Claim.

Due process prohibits the criminal prosecution of a defendant who is not competent to stand trial, and the state must provide procedures for determining the defendant’s competence. Medina v. California, 505 U.S. 437, 449, 112 S.Ct. 2572, 120 L.Ed.2d 353 (1992) (citing Drope v. Missouri, 420 U.S. 162, 172-73, 95 S.Ct. 896, 43 L.Ed.2d 103 (1975), and Pate v. Robinson, 383 U.S. 375, 386, 86 S.Ct. 836, 15 L.Ed.2d 815 (1966)). A state trial judge must conduct a competency hearing, regardless of whether defense counsel requests one, whenever the evidence before the judge'raises a bona fide doubt about the defendant’s competence to stand trial. *604 Odie v. Woodford, 238 F.3d 1084, 1087 (9th Cir.2001) (citing de Kaplany v. Enomoto, 540 F.2d 975, 979 (9th Cir.1976) (en banc)); see also Pate, 383 U.S. at 385, 86 S.Ct. 836 (finding the statutory procedure using the “bona fide doubt” standard to be constitutionally adequate). A bona fide doubt exists if there is “ ‘substantial evidence of incompetence,’ ” Amaya-Ruiz v. Stewart, 121 F.3d 486, 489 (9th Cir.1997) (quoting United States v. Lewis, 991 F.2d 524, 527 (9th Cir.1993)), or substantial evidence that the defendant lacks “sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding” or “a rational as well as factual understanding of the proceedings against him.” Dusky v. United States, 362 U.S. 402, 402, 80 S.Ct. 788, 4 L.Ed.2d 824 (1960) (per curiam); see also Torres v. Prunty, 223 F.3d 1103, 1106 (9th Cir.2000).

In reviewing whether a state trial judge should have sua sponte conducted a competency hearing, a federal court may consider only the evidence that was before the trial judge. United States v. Lewis, 991 F.2d 524, 527 (9th Cir.1993). Although no particular facts signal a defendant’s incompetence, suggestive evidence includes the defendant’s demeanor before the trial judge, irrational behavior of the defendant, and available medical evaluations of the defendant’s competence to stand trial. Drope, 420 U.S. at 180, 95 S.Ct. 896; Amaya-Ruiz, 121 F.3d at 489; Moran v. Godinez, 57 F.3d 690, 695 (9th Cir.1994).

To support his procedural-due-process claim, Williams relies upon a portion of a preliminary-hearing transcript that shows him failing to respond to questioning by the trial judge. The transcript reads as follows:

THE COURT: And I think that you personally do not have the money, Mr. Williams, to hire an attorney; is that right? You don’t have a bank account where you can go out and pour out the dough, right?

THE DEFENDANT: (The defendant shakes his head negatively.)

THE COURT: You better say “no” so the lady can put it down. Do you want to speak up? Mr. Williams? Did you understand what I’m saying, Mr. Williams?

THE DEFENDANT: (No audible response.)

THE COURT: Does he get in these moods frequently, Mr. Holiwell, where he won’t speak?

MR. HOLIWELL: Well, he’s been on PCP. And ever since then, he really been [sic] — since then he just haven’t [sic] been on alert. He go [sic] into strange moods.

THE COURT: All right. Well, I am aware that at least he’s alert and looking at me. And he’s not choosing to respond to my words. But I can’t say he’s understanding what I say.

MR. HOLIWELL: Can I speak to him?

THE COURT: Yes. Go ahead.

MR. HOLIWELL: Stan, you have to say something to tell the lady what you want to do. Tell the judge what you want to do.

DEFENDANT: What was the question?

THE COURT: You do not have the money personally to hire your own attorney?

THE DEFENDANT: Unh-unh.

THE COURT: Okay. Thank you, Mr. Williams. Thank you, Mr. Holiwell.

After this colloquy, Fred Holiwell, Williams’s stepfather, notified the trial judge that Williams needed “some psychiatric help.” The trial judge responded that he would appoint psychiatrists to examine Williams. Subsequently, the trial *605 judge ordered two psychiatrists, Dr. Alfred Coodley and Dr. Michael Coburn, to interview Williams and report to the court on his competence to stand trial and on the validity of his insanity plea, which Williams later withdrew. 16

After conducting a psychiatric interview with Williams, and after reviewing the police report and the transcripts of the preliminary hearings, Dr. Coodley concluded that Williams was neither incompetent to stand trial nor insane at the time of the alleged offenses. Dr. Coodley reported to the trial judge that Williams “is presently able to understand the nature and purpose of the proceedings taken against him. He is presently able to cooperate in a relatively rational manner with counsel in presenting a defense.” Dr. Coodley also informed the court that he “[did] not feel there is sufficient evidence to state that the defendant was insane by the A.L.I. rule at the time of commission of the alleged offenses.”

Dr. Coburn likewise reviewed the police report and the preliminary-hearing transcripts, but conducted only a limited interview with Williams. Unbeknownst to Dr. Coburn at the time of the interview, Williams had recently withdrawn his insanity plea. Thus, Williams declined to speak with Dr. Coburn about the alleged offenses, as he had with Dr. Coodley, until he consulted with his attorney. However, Williams did provide Dr.. Coburn with some background history. Dr. Coburn reported to the trial judge that, although he did not have sufficient data to draw conclusions with reasonable certainty, his preliminary impression was that there was little support for an insanity or diminished-mental-capacity defense.

Given these psychiatric evaluations by Drs. Coodley ' and Coburn, we conclude that the trial judge’s decision not to hold a competency hearing was not unreasonable. These evaluations could properly dispel any doubt that the judge had at the preliminary hearing regarding Williams’s competence to stand trial. Although Dr. Coburn did not provide a medical opinion that Williams was competent, as had Dr. Coodley, Williams’s unwillingness to discuss the alleged offenses with Dr. Coburn after the withdrawal of his insanity plea, and without first consulting with his attorney, showed that Williams had a rational and factual understanding of the proceedings against him. Williams’s comprehension of - the legal significance of the withdrawal of his insanity plea also indicated that he had the ability to consult with his attorney with a reasonable degree of rational understanding. See Dusky, 362 U.S. at 402, 80 S.Ct. 788 (competence is a rational and factual understanding of the proceedings and an ability to consult with defense counsel in a reasonably rational manner).

We also find relevant that the transcripts of the- police interview with Williams -and the proceedings before the trial court do not. evidence any bizarre or irrational behavior by Williams. See Drope, 420 U.S. at 180, 95 S.Ct. 896 (a defendant’s irrational behavior is a factor *606 to be considered in assessing competence); compare Chavez v. United States, 656 F.2d 512, 519 (9th Cir.1981) (a bona fide doubt existed as to the defendant’s competence when he fired his attorneys, had emotional outbursts resulting in his forcible removal from the courtroom, and did not attempt to plea bargain); United States v. Auen, 846 F.2d 872, 878 (2nd Cir.1988) (a bona fide doubt existed when the defendant exhibited bizarre behavior and beliefs in his pre-arrest correspondence with the government, in his post-arrest statements, and when before the court). Moreover, Williams’s defense counsel at no point raised the issue of Williams’s competence to stand trial. We have previously noted that “defense counsel [is] in the best position to evaluate [a defendant’s] competence and ability to render assistance.” Torres, 223 F.3d at 1109 (citing Medina, 505 U.S. at 450, 112 S.Ct. 2572); see also Hernandez v. Ylst, 930 F.2d 714, 718 (9th Cir.1991) (“We deem significant the fact that the trial judge, government counsel, and [the defendant’s] own attorney did not perceive a reasonable cause to believe[the defendant] was incompetent.”).

Williams argues that the trial court erred in failing to conduct a competency hearing, pointing to evidence that he seemed dazed and generally inattentive after his arrest and during trial. Much of the evidence that Williams cites was not before the trial judge, and so we do not consider it in deciding Williams’s procedural-due-process claim. See Lewis, 991 F.2d at 527 (only the evidence before the trial judge is relevant). To the extent that Williams’s dazed or inattentive demeanor was before the trial judge, we agree with the Eleventh Circuit that “there is no constitutional prohibition against the trial and conviction of a defendant who fails to pay attention in court— whether out of indifference, fear, confusion, boredom, or sleepiness — unless that defendant cannot understand the nature of the proceedings against him or adequately assist counsel in conducting a defense.” Watts v. Singletary, 87 F.3d 1282, 1287 (11th Cir.1996) (no bona fide doubt as to a defendant’s competence, even though he slept through approximately 70% of his murder trial, because he was able to provide lucid and rational answers when awake that demonstrated his understanding of the proceedings against him, and defense counsel never suggested that the defendant was incompetent). The trial transcript does not indicate that Williams lacked understanding of the proceedings or was unable to assist in his defense. To the contrary, the transcript shows that Williams informed the court that he did not want to testify at the penalty phase, and that he conferred with defense counsel regarding whether to call other witnesses at the penalty phase. The transcript also reflects that Williams was able to use somewhat technical legal terms appropriately (i.e., “Could I have [an attorney] appointed for right now?,” “I’d like to move for a continuance at this time because the attorney of my choice, he’s at this moment downtown fighting a murder trial.”). Thus, we conclude that any lack of attentiveness by Williams before the trial judge did not create a bona fide doubt about his competence.

Williams also contends that the trial judge unreasonably relied upon the psychiatric reports of Drs. Coodley and Coburn, asserting that neither doctor had the necessary family or background information to prepare a complete mental-status evaluation. We disagree. Although Dr. Co-burn’s opinion was admittedly tentative due to his limited interview with Williams, Dr. Coodley conducted a fairly comprehensive interview, questioning Williams about the alleged offenses, his childhood, family, medical history, schooling, drug use, and *607 other subjects. Thus, the trial judge reasonably relied upon Dr. Coodley’s medical opinion that Williams was competent to stand trial. We decline to consider the 1995 declarations of Drs. Coodley and Co-burn, and other evidence that Williams amassed during his habeas corpus proceedings to cast doubt on the validity of the doctors’ 1979 psychiatric reports, because this evidence was not available to the trial judge. See Lewis, 991 F.2d at 527 (we consider only the evidence that was before the trial court).

In sum, the trial judge afforded all the process due to make reasonably certain that Williams was competent to stand trial. The evidence before the trial judge did not require a formal competency hearing. However, whether Williams was in fact competent is a separate question, to which we now turn.

2. Substantive-Due-Process Claim.

On appeal, Williams challenges the scope of the district court’s evidentiary hearing on his claim that he was unconstitutionally tried while incompetent, and also the district court’s conclusion that Williams did not meet his burden of establishing his incompetence. See Williams IV, 41 F.Supp.2d at 1060.

(a) The Scope of the Evidentiary Hearing on Incompetence.

After reviewing Williams’s evidence that he was tried while incompetent, the district court was inclined to grant the state’s motion for summary judgment on the claim. See Williams III, 48 F.Supp.2d at 993. However, because the court had ordered an evidentiary hearing on the issue of Williams’s mental state in conjunction with his ineffective-assistance-of-eounsel claims, the district court denied the state’s motion, permitting further exploration of Williams’s substantive-due-process claim at the hearing already scheduled. See id.

At this hearing, the district court received direct testimony via narrative statement and also live testimony from Williams’s trial attorney, another attorney who represented Williams at the preliminary hearings, and a trial juror. See Williams IV, 41 F.Supp.2d at 1046. Although the parties moved the court to present the oral testimony of mental-health experts on the issue of Williams’s mental state, the district court instead ordered the parties to cross-examine the experts’ declarations by deposition and then file briefs detailing areas of possible impeachment. See id. Based upon the live testimony presented at the hearing and the declarations, depositions, and briefs filed by the parties, the district court denied Williams’s substantive-due-process claim. See id. at 1060.

Williams argues that the district court abused its discretion when it limited the scope of the evidentiary hearing on his incompetence claim in the above-described manner. Particularly, Williams contends that the hearing was inadequate without the oral testimony of expert witnesses, and that the court impermissibly resolved credibility questions and the merits of his claim on the basis of a predominantly written record.

As we discussed in the context of the hearing on Williams’s shackling claim, a district court in a habeas corpus proceeding has the discretion to conduct an evi-dentiary hearing by choosing a middle path that includes documentary evidence, but excludes oral testimony. See Watts, 841 F.2d at 277. A district court must only give the petitioner full opportunity to present the relevant facts. Id. Because Williams fails to identify any relevant facts that he was unable to present due to his inability to elicit oral testimony, we con- *608 elude that the district court did not abuse its discretion in restricting, as it did, the scope of the evidentiary hearing on his substantive-due-process claim.

(b) The Merits of Williams’s Substantive-Due-Process Claim.

To establish a violation of his right not to be tried and convicted while incompetent, Williams must show that at the time of trial he lacked either sufficient ability to consult with his lawyer with a reasonable degree of rational understanding, or a rational and factual undérstanding of the proceedings against him. See Dusky, 362 U.S. at 402, 80 S.Ct. 788. In deciding Williams’s claim of actual incompetence, we may consider facts and evidence that were not available to the state trial court before and during trial. See Watts, 87 F.3d at 1290; Boag v. Raines, 769 F.2d 1341, 1343 (9th Cir.1985). However, we disfavor retrospective determinations of incompetence, and give considerable weight to the lack of contemporaneous evidence of a petitioner’s incompetence to stand trial. Moran, 57 F.3d at 696.

In evaluating Williams’s substantive-due-process claim after the state’s motion for summary judgment and again after the evidentiary hearing on Williams’s mental state, the district court set forth in its opinions very thorough and detailed descriptions of the evidence that Williams presented in support of his claim. See Williams III, 48 F.Supp.2d at 990-93; Williams IV, 41 F.Supp.2d at 1052-59. We incorporate these descriptions by reference into our opinion. We review the district court’s credibility determinations for clear error, Fisher v. Roe, 263 F.3d 906, 912 (9th Cir.2001), and the district court’s competency determination de novo. Boag, 769 F.2d at 1343. We agree with the district court that Williams fails to establish his incompetence at the time of trial.

We find especially relevant defense counsel’s opinion that Williams was competent to stand trial. See Medina, 505 U.S. at 450, 112 S.Ct. 2572 (“defense counsel will often have the best-informed view of the defendant’s ability to participate in his defense”); Hernandez, 930 F.2d at 718 (the fact that defense counsel considered the defendant competent to stand trial was significant evidence that the defendant was competent). At the evidentiary hearing on Williams’s mental state, Joseph Ingber, Williams’s trial attorney, testified that Williams fully understood the nature of the proceedings against him and appropriately assisted with and made decisions regarding his defense. For example, Williams contributed to his alibi defense by providing Ingber with the names of the persons that he had been with at the time of the alleged offenses. Williams also indicated that he comprehended the ramifications of his decision not to call witnesses to provide mitigating evidence at the penalty phase. Ingber testified that Williams’s response to the proceedings against him was not at all unusual, that Williams exhibited no traits suggestive of mental illness, and that Williams engaged in normal conversations about subjects unrelated to the case that interested him, such as sports and weightlifting. Ingber roundly rejected the suggestion that Williams was incompetent at trial, stating that “there isn’t one scintilla of evidence anywhere during the course of this trial that indicates that Stanley Williams was not competent, if he wanted to, to assist in the preparation of this case.”

Ingber’s opinion regarding Williams’s competence is consistent with the evidence of Williams’s demeanor before the state trial court and the medical evaluations given to that court, which we have already *609 discussed in conjunction with Williams’s procedural-due-process claim. Ingber’s opinion also corresponds with Dr. Ronald Siegel’s 1979 mental-health report provided to defense counsel, which we may properly consider in resolving Williams’s claim of actual incompetence. See Boag, 769 F.2d at 1343. Dr. Siegel, as a psycho-pharmacologist, specialized in the study of how drugs affect the mind. He reviewed the police report, preliminary-hearing transcripts, and evaluations of Drs. Cood-ley and Coburn, and also conducted a four-hour examination of Williams. Dr. Siegel found that Williams “exhibit[ed] none of the characteristic changes in perception and body imagery associated with chronic PCP users, suggesting that his use of this compound has .been somewhat exaggerated or involves very low dosages.” Dr. Siegel reported “no indication of psychotic or schizophrenic thinking” and no “underlying psychopathology although [Williams] is extremely violent and assaultive.” Dr. Siegel concluded that Williams “was neither insane, unconscious, nor severely diminished in capacity ‘at"the time of the alleged offense. He was capable of knowing and understanding the nature and quality of his acts and the consequences.” We accord substantial weight to Dr. Sie-gel’s contemporaneous opinion that Williams did not suffer from a mental defect, and to the other evidence before the state trial court that suggested Williams was competent to stand trial. See Moran, 57 F.3d at 696 (noting that “medical reports contemporaneous to the time of the initial hearing greatly increase the chance for an accurate retrospective evaluation of a defendant’s competence”).

We give little weight to the declarations of the mental-health experts that Williams submitted in his habeas corpus proceedings. -The district court found that the declarations were not very credible, and this credibility determination is not clearly erroneous. The district ■ court correctly noted that the declarations fail to support sufficiently their retrospective assessments of Williams’s mental state by tying them to the facts of the case. See Williams IV, 41 F.Supp.2d at 1059 (“Petitioner’s experts did not adequately explain the effect of his impairments on his thoughts or actions, and failed to adequately explain how he could appear lucid during the crimes yet be unable to form the intent to kill”). The declarations do not describe how Williams’s probable mental impairment interfered with his understanding of the proceedings- against him or with.his ability to assist counsel in presenting a defense. With the exception of the incident , at the preliminary hearing where Williams stood mute- when questioned by the court, an incident that might simply have been a lapse in attention, the declarations do not point to any manifestation of Williams’s incompetence in the trial-court record. The declarations likewise fail to explain Williams’s rational responses to police questioning, his sensible decision not to speak with Dr. Coburn about the charged offenses after withdrawing his insanity plea, and his logical requests that the court appoint interim counsel and also continue the proceedings until his attorney was present, requests that reflect an understanding of the judicial proceedings. We agree with the district court that the declarations prepared by the mental-health experts for Williams’s habeas corpus proceedings are not entirely credible.

We also accord little weight to the competency assessments of Williams’s- habeas corpus experts because they are based not upon medical reports contemporaneous to the time of the preliminary hearings or trial, but upon declarations submitted by Williams’s friends and family and neurop-sychological testing conducted more than ten years after trial. We have previously *610 held that retrospective competency determinations, although disfavored, are permissible when it is possible to make an accurate retrospective evaluation, for example, by consulting contemporaneous medical reports. See Moran, 57 F.3d at 696. Without the benefit of such contemporaneous reports, the passage of time and the difficulties inherent in evaluating the defendant’s competence from a written record reduce the likelihood of an accurate retrospective determination. See Pate, 383 U.S. at 387, 86 S.Ct. 836 (concluding that no meaningful retrospective competency determination could be made six years after trial). Because we doubt the accuracy of the retrospective competency determinations of Williams’s habeas corpus experts, we conclude that the determinations are not especially probative of whether Williams actually was incompetent at the time of his trial.

Given the significant contemporaneous evidence of Williams’s competence at trial, supported by defense counsel’s firm belief that Williams was competent, and the absence of persuasive evidence to the contrary, Williams fails to establish a violation of his right not to be tried and convicted while incompetent. We affirm the district court’s denial of both Williams’s procedural-due-process and substantive-due-process claims.

F. Ineffective Assistance of Counsel. (Claim D)

Williams argues that the district court erred in denying on summary judgment his claim that defense counsel was ineffective at the guilt phase of trial. See Williams III, 48 F.Supp.2d at 1000. To prevail on his claim, Williams must first show that defense counsel’s representation fell below an objective standard of reasonableness under prevailing professional norms. Strickland v. Washington, 466 U.S. 668, 688, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Williams faults Ingber for insufficient investigation of a mental-state defense and for his decision not to pursue the defense at the guilt phase. “[C]ounsel has a duty to make reasonable investigations or to make a reasonable decision that makes particular investigations unnecessary.” Id. at 691, 104 S.Ct. 2052. “[Strategic choices made after less than complete investigation are reasonable precisely to the extent that reasonable professional judgments support the limitations on investigation.” Id. at 690-91, 104 S.Ct. 2052. In assessing the reasonableness of Ing-ber’s representation, we must be “highly deferential,” avoid “the distorting effects of hindsight,” and “indulge a strong presumption that [his] conduct falls within the wide range of reasonable professional assistance.” Id. at 689, 104 S.Ct. 2052.

In a declaration submitted in the state habeas corpus proceedings, Ingber explained that he did not present a mental-state defense because he had no credible evidence of mental disability or brain damage to support such a defense. When Ingber inherited Williams’s case from pri- or counsel, three mental-health experts had already interviewed Williams and reviewed the police report and preliminary-hearing transcripts. As already discussed in the context of Williams’s competency claims, Dr. Siegel provided his “considered opinion” that Williams “was neither insane, unconscious, nor severely diminished in capacity at the time of the alleged offense.” Dr. Coburn’s “preliminary impressions based on the materials at hand and [his] examination of [Williams did] not indicate any support for [a] defense position of insanity or diminished capacity, unless virtually all of the witness statements regarding both [Williams’s] behavior and his post-offense statements [were] discounted completely.” Dr. Coburn reported that *611 “[t]here [was] really nothing in the data itself to support the likelihood that [Williams’s] behavior or thought patterns were materially affected by any POP usage.” Dr. Coodley concluded that Williams was sane, but noted the “possibility] that [his] mental capacity to form the specific intent to kill, rob and kidnap at the time of the commission of the alleged offenses was diminished because of POP (angel dust) use.” However, Dr. Coodley stated that he did “not have sufficient tangible evidence to support that conclusion [of diminished mental capacity].”

“In general, an attorney is entitled to rely on the opinions of mental health experts in deciding whether to pursue an insanity or diminished capacity defense.” Hendricks v. Calderon, 70 F.3d 1032, 1038 (9th Cir.1995); see also Harris v. Vasquez, 949 F.2d-1497, 1525 (9th Cir.1990) (“It is certainly within the ‘wide range of professionally competent assistance’ for an attorney to rely on properly selected experts.”). We have previously held that defense counsel reasonably declined to pursue a mental-state defense when two experts opined that the defendant was neither insane nor diminished in mental capacity, and a third expert could not reach a conclusion. Morgan v. Bunnell, 24 F.3d 49, 52 (9th Cir.1994); see also Hendricks, 70 F.3d at 1038 (defense counsel was not deficient in deciding not to present a mental-state defense when two mental-health experts had found no evidence that the defendant was insane or diminished in mental capacity). Moreover, it is “acceptable trial strategy to choose not to call psychiatrists to testify when they can be subjected to cross-examination based on equally persuasive psychiatric opinions that reach a different conclusion.” Harris, 949 F.2d at 1525. Given that the mental-health experts’ evaluations of Williams did not support a mental-state defense, Ingber’s decision not to investigate further or ultimately pursue the defense was a reasonable strategic choice. See Strickland, 466 U.S. at 690-91, 104 S.Ct. 2052.

Ingber’s conclusion that an alibi defense was both viable and preferable to a mental-state defense also cannot be criticized. In response'to questioning by the police, Williams had insisted that he was not present at either of the two robbery-shootings, and had disputed the statements of the government informants that he had admitted responsibility for the crimes.

Williams had similarly denied involvement in the crimes during his mental-health consultations with Drs. Coodley and Siegel. In an interview with the police, Holiwell, Williams’s stepfather, had stated that he saw Williams at a bar right before the Brookhaven Motel crimes occurred, thereby indicating that Williams'could not have been the perpetrator. Williams provided Ingber with the names of other witnesses, like Beverly McGowan and Eugene Riley, who were able to substantiate Williams’s alibi defense by testifying that he was with them at the time of the alleged offenses. The credibility of the prosecution’s witnesses that placed Williams at the crime -scenes was suspect because they each had inducements to testify. Ingber could through cross-examination bring out their motivations to- lie. Given this factual support for the alibi defense, “[i]t was clearly within the ‘wide range of professionally competent assistance’ for [Ingber] to choose not to present a psychiatric defense theory that could conflict with [the] alibi .defense.... ” Harris, 949 F.2d at 1525.

Having reasonably selected an alibi defense as the primary defense theory, Ing-ber no longer had a duty to investigate a conflicting mental-state defense. See Bean v. Calderon, 163 F.3d 1073, 1081-82 *612 (9th Cir.1998) (counsel’s reasonable choice of an alibi defense ended counsel’s duty to investigate a conflicting defense of diminished mental capacity); Turk v. White, 116 F.3d 1264, 1266-67 (9th Cir.1997) (defense counsel’s reasonable selection of a self-defense theory obviated counsel’s need to investigate a conflicting defense of incompetency); Correll v. Stewart, 137 F.3d 1404, 1411 (9th Cir.1998) (defense counsel was not ineffective for failing to present psychiatric evidence that would have contradicted the primary defense theory of misidentification); Fritchie v. McCarthy, 664 F.2d 208, 215 (9th Cir.1981) (same).

Williams argues that Ingber’s decision to pursue an alibi rather than a mental-state defense was not a considered choice, and that Ingber simply “tossed out whatever came to hand, irrespective of merit.” to support this inference, Williams points to aspects of Ingber’s pre-trial representation, for example, that Ingber informed the prosecutor of his intention to present an alibi defense only the day before trial began; that Ingber denied on the record that Holiwell, Williams’s stepfather, definitively would be a defense witness when later he was the first alibi witness called for the defense; and that Ingber refused, in advance of trial, to request or reject jury instructions on diminished mental capacity, and then failed to inform the prosecutor whether this refusal was “inadvertence or trial tactics.”

Our review of the record reveals that the inference that Williams argues — that Ingber’s reticence to disclose information about the defense strategy evidences Ing-ber’s lack of preparation and ill-considered choice of defense strategy — is not supportable. Ingber informed the prosecutor on the day before trial of his intent to present an alibi defense only to comply with California Penal Code § 1051 (1981), which Ingber understood to require such notice and to allow the prosecutor to seek a continuance if the state did not receive the necessary notice. Ingber did divulge the names of some defense witnesses before trial in order to allow the court to rule on the admissibility of the witnesses’ prior convictions. Ingber also revealed the identity of some defense witnesses prior to trial when he made arrangements to have various inmates released from custody so that they could testify in court. When the prosecutor sought the names of all the witnesses that the defense planned to call, Ingber refused, arguing to the trial court: “[I]f I were to reveal the names of alibi witnesses, I would be subject [to sanctions] for inadequacy of counsel and incompetency and possibly malpractice.” When Ing-ber declined to express a preference regarding jury instructions on diminished mental capacity in advance of trial, the prosecutor attributed this conduct to trial tactics, not inadvertence. Referring to an award recently presented to Ingber for his outstanding work as a trial attorney, the prosecutor said: “I would assume that the record should reflect that that is being done as a means of trial tactics by what is certainly known in this area as a very prestigious and competent attorney, Mr. Joseph Ingber, the recipient of the Jerry Geisler Award by the Criminal Courts Bar Association.” In light of this record, we conclude that the inference that Williams asserts, namely that Ingber arbitrarily chose a defense strategy without regard to merit, is not a reasonable one. The conduct that Williams highlights suggests only that Ingber was being cagey about disclosing his defense strategy to the prosecution.

Because Ingber made a reasonable strategic decision to present an alibi defense and not a mental-state defense, Williams fails to establish that Ingber’s representation was deficient. See Strickland, 466 U.S. at 687, 104 S.Ct. 2052. We affirm the district court’s grant of summary judg *613 ment on the basis that defense counsel was effective at the guilt phase of trial. 17

G. Cumulative Error.

“Although no single alleged error may warrant habeas corpus relief, the cumulative effect of errors may deprive a petitioner of the due process right to a fair trial.” Karis, 283 F.3d at 1132. That is not the case here. Williams has not shown that the cumulative prejudicial effect of the alleged errors at his trial puts the case in such a different light as to undermine confidence in its outcome. See Kyles v. Whitley, 514 U.S. 419, 434-35, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995).

II. Penalty-Phase Challenges.

A. Ineffective Assistance of Counsel. (Claims Q & R)

Williams argues that his defense counsel’s performance during the penalty phase was ineffective because counsel failed to investigate and present mitigating evidence. Williams contends that Ingber did not sufficiently investigate his family and life history, drug use, and mental state. Williams also asserts that no reasonable tactical decision supported Ingber’s failure to present any mitigating evidence to the jury-

As with his guilt-phase claim, Williams must first establish that Ingber’s representation was deficient, or in other words, that it fell below an objective standard of reasonableness under prevailing professional norms. Strickland, 466 U.S. at 687-88, 104 S.Ct. 2052. Although counsel is under a duty to make reasonable investigations, counsel may make a reasonable decision that particular investigations are unnecessary. Id. at 691, 104 S.Ct. 2052. Thus, “counsel’s decision not to mount an all-out investigation into petitioner’s background in search of mitigating circumstances” is not deficient when it is “supported by reasonable professional judgment.” Burger v. Kemp, 483 U.S. 776, 794, 107 S.Ct. 3114, 97 L.Ed.2d 638 (1987). We apply “a heavy measure of deference to counsel’s judgments.” Strickland, 466 U.S. at 691, 104 S.Ct. 2052. However, our “deference to counsel is predicated on counsel’s performance of sufficient investigation and preparation to make reasonably informed, reasonably sound judgments.” Mayfield, 270 F.3d at 927 (citing Strickland, 466 U.S. at 691).

1. Ingber’s Investigation Was Sufficient To Support His Reasonable Decision Not To Present Mitigating Evidence.

Although the exact parameters of Ingber’s investigation and preparation for the penalty phase are unknown due to the loss of his original trial file 18 and the passage of time, the record nonetheless shows that he did investigate evidence regarding Williams’s family and life history, drug use, and mental state with an eye *614 towards using it at the penalty phase. 19 In researching and preparing for the case, Ingber spoke extensively with Williams, visiting him in jail many times, and also with Williams’s mother and step-father, with whom Ingber was in frequent contact. Ingber interviewed a number of witnesses suggested by Williams, and hired at least one investigator to subpoena witnesses and collect information relevant to the case. Ingber reviewed the entire case file provided him by Williams’s prior counsel, the mental-health evaluations submitted by Drs. Coodley, Coburn, and Siegel, 20 and the police “murder books” regarding the 7-Eleven and Brookhaven Motel murders, which contained interview transcripts, arrest reports, investigative reports, and autopsy reports. In accordance with his regular custom and practice, Ing-ber also compiled a client history, which included information about Williams’s background, inclinations, police arrest record, and the arrest at issue in the case. Ingber put together this client history because, in his experience, 21 he found it to be especially useful in preparing for the penalty phase of trial. However, Ingber did testify that the client history that he compiled in Williams’s ease was less extensive than the client history that he would normally assemble because, as the fifth or sixth attorney to work on Williams’s case, Ingber’s time frame for compiling the history was shorter than usual.

Based upon these investigative efforts, Ingber was aware of aspects of Williams’s family and life history, drug use, and mental state. There was some evidence of turbulence in Williams’s family relationships. Williams’s mother was a dominant presence throughout much of his childhood. Williams fought frequently with his sister during childhood because he believed that his mother preferred her. Williams’s father never lived with the family, and Williams felt anger towards his father, informing Dr. Coodley that he would attack his father if he saw him. Williams’s mother remarried when he was fourteen, and Williams got along very well with his step-father. Williams had many girlfriends, and had two children with one of them.

Ingber knew of evidence of Williams’s drug use and psychiatric history, but believed the evidence to be weak. Williams suffered head injuries as a child from running into a door on one occasion and a monkey bar on another. Williams sniffed glue and smoked marijuana as a teenager. In his twenties, Williams became a regular *615 user of first LSD and later PCP. Williams was involuntarily committed to a state hospital at one point; however, Williams indicated that his drug use was the likely reason for this hospitalization. Williams’s step-father informed Ingber that Williams had participated in group therapy sessions, but Williams told Dr. Coodley that he had skipped the sessions at the outpatient mental-health clinic that he was to attend after his hospitalization. Coward’s statements to the police showed that Williams had smoked Sherms before the 7-Eleven robbery-murder, and Dr. Coodley’s report flagged the possibility that Williams’s mental capacity was diminished at the time of the offenses because of PCP use. However, Dr. Coodley concluded that Williams was sane, and both Drs. Coburn and Siegel found no evidence to support a mental-state defense. Furthermore, no lay witness that Ingber interviewed provided any facts suggesting that Williams’s PCP use had the specific effect of diminishing his mental capacity at or near the times of the crimes.

Ingber also learned of Williams’s gang involvement from Williams and the police interviews transcribed in the “murder books.” Williams related to Ingber that he had been a member of the Crips for years, and that all of his friends were Crips. According to Williams, the police had stopped him and his companions on a number of occasions, and filled out field interview cards that identified them as gang members. From his conversations with Williams, Ingber formed the impression that Williams’s gang involvement “wasn’t a coerced part,” but rather “was a fun part of his life.” In his Mirandized post-arrest interview with the police, Williams admitted that “he used to be the leader, not the follower, ... of the west-side” Crips. James Garrett also informed the police in a recorded interview that Williams was “one of the top ... gang leaders ... Crips there is- [H]e’s respected by all the Crips, and hated by all the other gangs, the Pirus, the Top Hats, or whatever.” Garrett stated that Williams made his reputation in “gang banging,” in fighting and killing members of other gangs. According to Garrett, no one could “really get a line on [Williams] for the simple reason that he puts fear ... in ... guy’s hearts.... That’s the type of guy he is.” Williams’s statements in his Mirandized interview with the police tended to confirm the image that Garrett painted. Williams said that “a lot of people hate me” because “I’m ... mean sometimes.” He claimed to be “real good” at”[a]ttacking people, [especially to [their] back.” He also answered that he “doubtfed] it” would “bother” him “if [he] ever killed anybody.”

Ingber’s investigation was sufficient to support his reasonable strategic decision that the presentation of evidence regarding Williams’s family and life history, drug use, or mental state at the penalty phase would not serve Williams’s interest. As we noted in the context of Williams’s guilt-phase claim of ineffective assistance of counsel, “strategic choices made after less than complete investigation are reasonable precisely to the extent that reasonable professional judgments support the limitations on investigation.” Strickland, 466 U.S. at 690-91, 104 S.Ct. 2052. The above-described results of Ingber’s investigation provided him with adequate basis for a reasonable professional judgment not to present mitigating evidence because (1) the evidence available was not especially helpful, (2) the presentation of mitigating evidence would open the door to damaging rebuttal evidence of Williams’s gang activities, (3) Williams specifically requested that no witnesses be called at the penalty phase, and (4) lingering doubt regarding Williams’s guilt was a viable defense. *616 Having made this reasonable strategic choice, Ingber cannot be faulted for any failure to investigate further or locate additional witnesses who would have made statements about Williams’s past. See Burger, 483 U.S. at 794-95, 107 S.Ct. 3114 (after evaluating the available mitigating evidence and reasonably deciding that the evidence would not have minimized the risk of the death penalty, and would have harmed the chances for a life sentence, counsel had no obligation to continue investigating the defendant’s background).

In support of his argument that Ingber failed sufficiently to investigate mitigating evidence for the penalty phase, Williams points to numerous lay-witness declarations amassed in his habeas corpus proceedings to show the mitigating evidence that Ingber allegedly could have presented. The state argues that many of these declarations are not part of the record on appeal because the district court did not admit them into evidence. We do not resolve whether these declarations are properly part of the appellate record because we need not consider them. “ ‘[T]he relevant inquiry under Strickland is not what defense counsel could have pursued, but rather whether the choices made by defense counsel were reasonable.’ ” Babbitt v. Calderon, 151 F.3d 1170, 1173 (9th Cir.1998) (quoting Siripongs v. Calderon, 133 F.3d 732, 736 (9th Cir.1998)). Ingber made a reasonable strategic choice not to present mitigating evidence based upon the investigation he conducted. Consequently, what he might have uncovered had he investigated further is not relevant.

2. Ingber Made A Reasonable Strategic Decision Not To Present Mitigating Evidence.

Turning to the four reasons that supported Ingber’s decision not to present mitigating evidence at the penalty phase, we now explain why these reasons made Ingber’s decision a reasonable penalty-phase strategy.;

(a) The Evidence Available Was Not Especially Helpful.

Ingber legitimately concluded that the available evidence regarding Williams’s family and life history, drug use, and mental state offered only weak mitigation, if that. At the federal evidentiary hearing, Ingber testified that the evidence of Williams’s troubled family background was by no means uniformly helpful because it suggested violent propensities that were at odds with the goal of portraying Williams as less culpable. For example, Dr. Cood-ley’s mental-health report to the court indicated that Williams often clashed with his sister because he believed his mother favored her, and that he resented his absent father, whom he wanted to attack. Ingber noted that, on the one hand, these family relationships “could have created some type of psychological problems” that would make Williams seem less blameworthy. On the other hand, Ingber did not “want th[e] jury to hear that [Williams] wants to attack his father and [has] this ongoing hostility with his sister.” Ingber made a reasonable strategic decision to keep these potentially damaging facts from the jury. See id. at 793, 107 S.Ct. 3114 (counsel was not deficient for failing to present “information about petitioner’s troubled family background that could have affected the jury adversely by introducing facts [suggesting violent tendencies and encounters with law enforcement authorities] not disclosed by his clean adult criminal record”).

Ingber also exercised reasonable professional judgment in concluding that a penalty-phase defense that relied upon Williams’s drug use and mental state was not practicable, and would have detracted *617 from a viable defense strategy that capitalized on any lingering doubt that the jury might have had regarding Williams’s guilt. Ingber testified that a defense of diminished mental capacity was “raisable,” but not “potentially sellable to a jury” because it lacked support in the opinions of the mental-health experts that examined Williams and in the facts of the case. Although Dr. Coodley had indicated a possibility of diminished mental capacity at the time of the alleged offenses due to PCP use, Ing-ber believed that any testimony by Dr. Coodley, or any other psychiatrist, about Williams’s diminished mental capacity would be subject to persuasive expert testimony to the contrary. The prosecutor had notice of the appointment of Drs. Co-burn and Siegel, both of whom had rejected a conclusion of Williams’s diminished mental capacity from drug use. From the failure of the defense to call Drs. Coburn or Siegel as witnesses, the prosecutor could infer that their opinions were not favorable to the defense. Based upon his experience, Ingber knew that the prosecutor would likely subpoena these appointed experts to rebut any claim of Williams’s diminished mental capacity at the time of the offenses. We do not question Ingber’s professional judgment on this matter because “£i]t is ... acceptable trial strategy to choose not to call psychiatrists to testify when they can be subjected to cross-examination based on equally persuasive psychiatric opinions that reach a different conclusion.” Harris, 949 F.2d at 1525.

Furthermore, Ingber respected Dr. Co-burn’s opinion that the witness statements to the police provided no basis for believing that PCP materially affected Williams’s behavior or thought patterns at the time of the crimes. The facts of the crimes reflected deliberate and methodical action. The prosecution’s witnesses testified that Williams shot out the television monitor at the 7-Eleven, killed witnesses to the crimes, • and then picked up the expended shotgun shells all to escape detection. In Ingber’s experience, a jury would not find credible a claim of diminished mental capacity unless there was evidence of drug -use contemporaneous with the crimes and also a specific effect on the defendant’s state of mind. No lay witness that Ingber interviewed “was going to testify that Mr. Williams was materially affected by the use of ... PCP, that [PCP] caused his activities on the evening in question [and] prevented] him from having a specific intent to commit the robberies.” Given the facts of the crimes and the lack of credible evidence of contemporaneous drug use impacting Williams’s mental state, Ingber’s decision that a defense of diminished mental capacity was not feasible certainly fell “within the wide range of reasonable professional assistance.” Strickland, 466 U.S. at 689, 104 S.Ct. 2052.

Finally, Ingber reasonably concluded that presenting evidence in support of a nonviable diminished-mental-capacity defense would detract from a viable lingering-doubt defense. Ingber was “terribly reluctant to [present psychiatric evidence] because [he thought] it would ... diffuse whatever [they] had going for [them] on a lingering doubt concept.... It would be like [they] were just throwing everything up on the wall and ask[ing] the jurors [to pick a theory].” Ingber thought it better to focus the jurors’ attention on an argument that lingering doubt regarding Williams’s guilt counseled against a death-penalty verdict. As we discuss in more detail below, and as the district court aptly noted, a lingering-doubt strategy was viable because “[t]here were no eyewitnesses to the Brookhaven Motel murders and the only eyewitness to the 7-Eleven murder was an accomplice who had a strong motive to lie. The prosecutor’s case was based on circumstantial evidence and the *618 testimony of witnesses whose credibility was highly suspect.” Williams IV, 41 F.Supp.2d at 1052. We cannot fault Ing-ber’s reasonable strategic decision to capitalize on any lingering doubts of the jurors and to keep from them mental-state and drug-use evidence that might jeopardize their lingering doubts. . See Harris, 949 F.2d at 1525 (it was “professionally competent assistance for [counsel] to choose not to present a psychiatric defense theory that could conflict with ... his mitigation based on [the defendant’s] alleged remorse and his abusive childhood”) (internal quotations omitted); Siripongs v. Calderon, 133 F.3d 732, 736 (9th Cir.1998) (“defense counsel made a reasonable tactical decision to capitalize on any lingering doubts about [the defendant’s] actual involvement in the crimes themselves and to keep from the jury any evidence [in support of an accomplice defense] that [the defendant] had participated in the criminal activity”).

(b) The Presentation Of Mitigating Evidence Would Open The Door To Damaging Rebuttal ■ Evidence Of Williams’s Gang Activities.

Ingber exercised reasonable professional judgment when he decided not to present mitigating evidence because, in his words, “the vehicle of mitigation [could] create a worse picture than [had] already been presented, which was not good.” Under California Penal Code § 190.3, the prosecution was- required to give the defense notice before the start of the trial’s guilt phase of any evidence to be introduced in aggravation at the penalty phase. Prior to trial, the prosecution did not notice its intent to introduce any aggravating evidence, which to Ingber was “a cue that they think the case itself is aggravating enough.” Ingber then filed a motion, which was granted, to preclude evidence in aggravation because he had received no timely indication from the prosecution that they intended to present any. Knowing that the prosecution was thus bound to rely on the evidence of the guilt phase, Ingber was faced with the question of whether to present mitigating evidence, which would allow the prosecution to introduce evidence in rebuttal without any notice to the defense. See Cal.Penal Code § 190.3 (1981).

Ingber knew that the prosecution was aware of evidence of Williams’s gang affiliation, although Ingber did not know the exact scope of the evidence available to the prosecution. As outlined above, the “murder books” contained damaging admissions from Williams in his Mirandized police interview — that he was a leader of the westside Crips, and that he was “mean,” combative, and unmoved by the thought of killing another human being. James Garrett’s statements to the police about Williams’s gang activities were equally harmful, indicating that Williams was a top gang leader that, made his reputation in “gang banging.” Williams did not have a prior criminal record, and no gang evidence had come in at the guilt phase. However, Ingber had strong reason to believe that if he presented evidence in mitigation at the penalty phase, the prosecutor would seek to introduce gang .evidence in rebuttal.

Before trial, Ingber had brought to the court’s attention that “there has been numerous and repeated reference in the discovery, which was generously provided to [the defense] by [the prosecution], in interviews of witnesses concerning activity that could be described as gang activity. [Ing-ber] noted Mr. Murray and Mr. Garrett and Mr. Coleman and Mr. Coward.” Ing-ber argued that “[g]angs are not an issue in this case,” and requested that “those People’s witnesses be requested to refrain from voluntarily making such reference” to any gang activity. The prosecutor represented that “the People have no intention *619 at this time of introducing testimony concerning gangs, unless it comes out either from the psychiatric standpoint or the standpoint of the defense and rebuttal.” The prosecutor asserted that if Williams put his state of mind in issue, then his gang activities — particularly his own statements regarding his gang activities— would be relevant to his state of mind. The court decided that “before any statements are offered having to do with gang activity, that matter should be brought to the attention of the court so that [there] can [be] an appropriate ruling on the relevancy issue.” At that point, the court was “not in a position to say what is relevant and what is not.” In response to Ingber’s contention that Williams’s statements to the police about his gang affiliation were not voluntary, the court declared that “[i]f any statements of the defendant are going to be offered, of course, we have to have a hearing as to their voluntariness, and rights, and so on and so forth.”

Given this pre-trial argument before the court, Ingber had substantial basis for believing that any mitigating evidence proffered would meet with an offer of rebuttal evidence in the form of gang activity. If the defense presented sympathetic evidence to humanize Williams before the jury, then the prosecution would likely counter with gang evidence to portray him as a heartless killing machine. If the defense introduced evidence to suggest that Williams’s troubled family background or diminished mental capacity caused the offenses at issue, then the prosecution would probably present gang evidence to show that the offenses were part of Williams’s gang lifestyle, not the result of any family problems or diminished mental capacity. Ingber knew that the prosecution had available to it witnesses that cou'ld testify to Williams’s gang involvement because these witnesses had already testified for the state at the guilt phase. Moreover, Ingber noted that California law in 1981 broadly allowed for the admission of rebuttal gang evidence. Ingber was also of the opinion that the trial judge would admit the evidence because the judge “was quite liberal in allowing rebuttal evidence” and had given the prosecutor “a lot of elasticity throughout the trial.”

It was Ingber’s experience that when jurors are presented with evidence of gang activity, “they are likely to conclude that it is predominating rather than the mental defect or the diminished capacity.” Ing-ber was also “aware of the fact that the opportunity for the introduction of rebuttal evidence can be more devastating sometimes than the introduction of the evidence in aggravation.” In this case, Ingber thought that Coward and possibly the other men involved in the 7-Eleven robbery-murder were Crips members. Ingber feared that the introduction of rebuttal gang evidence, would allow the prosecution to depict the 7-Eleven robbery-murder as four gang members “leaving South Central Los Angeles and going out to Whittier,” which is about , twelve miles southeast of Los Angeles, “to execute the clerk by having him bend down in the back room and Mr. Williams shoot him in the back.” Ing-ber felt that portraying these crimes as part and parcel of gang life would only “expand[] an already horrendous situation.” Because by statute the prosecution could not present any evidence in aggravation, Ingber concluded that “[i]t was foolish” to present mitigating evidence that he “didn’t think would help [his] client, but would hurt him” by opening the door to damaging rebuttal evidence of his gang activities.

We do not second-guess Ingber’s reasonable professional judgment. The Supreme Court and this court have consistently held that counsel’s performance is not deficient for the failure to present *620 evidence in mitigation at the penalty phase when counsel’s decision is based upon a reasonable tactical determination that the mitigating evidence would allow for the introduction of rebuttal evidence “that might be literally fatal.” Burger, 483 U.S. at 791-94, 107 S.Ct. 3114 (counsel’s failure to present any mitigating evidence, including the defendant’s own testimony or the testimony of the defendant’s mother that he had an exceptionally unhappy and physically abusive childhood, or the expert testimony of a psychologist, was reasonable professional judgment because the testimony would risk bringing before the jury evidence of the defendant’s unremorseful attitude, violent tendencies, and prior criminal acts); see Strickland, 466 U.S. at 699, 104 S.Ct. 2052 (counsel’s decision not to present mitigating evidence of the defendant’s character or mental state was a reasonable strategic choice because (1) counsel could rely upon the defendant’s statements regarding his financial troubles, extreme emotional distress, and acceptance of responsibility for the crimes that came in at the plea colloquy, (2) the mitigating evidence would have been of little help, and (3) would have opened the door to damaging rebuttal evidence of the defendant’s criminal history and contrary opinions regarding the defendant’s character and mental state); Darden v. Wainwright, 477 U.S. 168, 186-87, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (counsel’s decision not to present character or mental-state evidence in mitigation, and instead to rely upon a simple plea for mercy from the defendant himself, was sound trial stratégy because the mitigating evidence would have opened the door to damaging rebuttal evidence of the defendant’s prior convictions, marital infidelity, and a psychiatric opinion that the defendant was a socio-pathic personality who was very capable of committing the crimes at issue); Siripongs, 133 F.3d at 736-37 (counsel reasonably decided not to present mitigating testimony from the defendant’s friends and family, particularly from his mother regarding his financial support of her and'his abusive and dysfunctional family life during childhood, because doing so would risk the introduction of rebuttal evidence of the defendant’s prior criminal conduct); Campbell v. Kincheloe, 829 F.2d 1453, (9th Cir.1987) (counsel’s failure to present any mitigating evidence, including evidence that the defendant had an alcoholic father, was a victim of child abuse, suffered from various medical problems as a child, had a history of drug and alcohol abuse, had attempted suicide, and was the father of two children, was a reasoned strategic choice because evidence in mitigation would have opened the door to devastating rebuttal evidence that he forcibly raped his ex-wife, repeatedly raped fellow inmates, was involved in drug and alcohol-induced violence, and participated in sexually abhorrent conduct with children and animals).

Moreover, we have previously recognized that in the early 1980s,. “evidence of criminal conduct alone, independent of a conviction, was admissible in California for a wide variety of purposes at the penalty phase,” and that the scope of admissible rebuttal evidence “was a ‘frequent source of uncertainty for both trial counsel and trial courts.’ ” Siripongs, 133 F.3d at 736 (quoting In re Jackson, 3 Cal.4th 578, 11 Cal.Rptr.2d 531, 835 P.2d 371, 394 (1992) (en banc)); see also People v. Gonzalez, 51 Cal.3d 1179, 275 Cal.Rptr. 729, 800 P.2d 1159, 1200 (1990) (en banc) (“the limits of permissible rebuttal were not so clear at the time of the defendant’s trials in 1980 and 1981”). Given this state of the law and Ingber’s experience that the trial judge liberally allowed rebuttal evidence, see Campbell, 829 F.2d at 1462-63 (deferring to counsel’s professional judgment, *621 based upon his experience and education, that the trial judge would deny any motion in limine to exclude the harmful rebuttal evidence), Ingber was understandably concerned that the judge would admit the prosecution’s damaging rebuttal evidence of Williams’s gang activities. Under the circumstances, Ingber made a reasonable tactical decision to leave the jury with the impression that Williams had no gang involvement, rather than risk introduction of gang evidence that in all likelihood would have overwhelmed the mitigating evidence presented.

Ingber also reasonably took into consideration his client’s desire that no witnesses be called to testify at the penalty phase. “The reasonableness of counsel’s actions may be determined or substantially influenced by the defendant’s own statements or actions.” Strickland, 466 U.S. at 699, 104 S.Ct. 2052. In accordance with his usual practice, Ingber broached the subject of penalty-phase witnesses with Williams in advance of the jury’s verdict in the guilt phase. Certain witnesses were available to the defense to provide mitigating testimony at the penalty phase, and Ingber thought it prudent to consider presenting evidence in mitigation in every case. Ingber explained to Williams that the purpose of introducing the witnesses’ testimony was “[t]o try to influence the jury to render a verdict of life without possibility of parole instead of the death penalty.” Nonetheless, Williams’s “feelings were intense about not calling anyone.” Williams did not want to testify himself, nor did he want any family members, friends, mental-health experts, or other potential witnesses to testify.

We reject Williams’s argument that he told Ingber only that he did not want his mother or step-father to testify, and that he put no restrictions on Ingber’s calling of other witnesses. The district court found specifically that Williams’s “prohibition was not limited to his mother and step-father, but included mental health experts and any other potential witness.” Williams TV, 41 F.Supp.2d at 1050. Support for. the district court’s factual finding exists in Ingber’s statements on the record before the trial court, in Ingber’s deposition conducted in conjunction with the federal habeas corpus proceedings below, and in Ingber’s testimony at the federal evi-dentiary hearing before the district court. Accordingly, the factual finding is not clearly erroneous. See Easley, 532 U.S. at 242, 121 S.Ct. 1452 (reversal of a district court’s factual finding is appropriate under the “clear error” standard only when “on the entire evidence” the appellate court is “left with the definite and firm conviction that a mistake has been committed”).

Before the penalty phase commenced, Ingber brought to the trial court’s attention Willliams’s opposition to calling witnesses to testify in mitigation. Ingber represented, “I do believe that I do have available to me witnesses who would help this jury make the ultimate determination. By the same token, I do have to regard the wishes of my client in connection with the noncalling of certain witnesses.” When Ingber requested that Williams state on the record whether he wanted to testify at the penalty phase, Williams responded, “Hell no.” Ingber also asked Williams to express his opinion “concerning the calling of certain other witnesses.” After a discussion held off the record, Ingber stated, “He is shaking his head and indicating to me it is his desire, his wish, that no other witnesses be called in the penalty phase.” The court recessed so that Ingber and Williams might confer further on the sub *622 ject. After the break, Ingber informed the court, “It’s the defendant’s desire that no one testify on his behalf in this phase, and I acquiesce to the desires of the defendant. So there will be no testimony called in this phase of the trial.” The trial court addressed Williams directly and strongly urged him to present mitigating evidence. When the court asked Williams whether he had enough time to discuss the matter with counsel, Williams declined to respond.

In the federal proceedings below, Ingber testified that Williams’s aversion to the calling of penalty-phase witnesses was only one of the factors that influenced Ingber’s ultimate decision not to present mitigating evidence. Ingber acknowledged, “It’s my job sometimes to overlook what [my clients] say and do what I think is in their best interest with my experience.” However, in this particular case, Ingber concluded that the factors converged. His assessment that the available mitigating evidence was weak and his trepidation that the prosecution would introduce damaging gang evidence in rebuttal, coupled with Williams’s resistance to the presentation 'of witness testimony, all persuaded Ingber to forsake mitigating evidence at the penalty phase and rely upon an argument that capitalized on any lingering doubts of the jurors regarding Williams’s guilt.

Although our case law “does not quite say that the defendant absolutely controls” counsel’s representation, Landrigan v. Stewart, 272 F.3d 1221, 1226 (9th Cir.2001), “[t]he client’s wishes are not to be ignored entirely.” Campbell, 829 F.2d at 1463; see also Gerlaugh v. Stewart, 129 F.3d 1027, 1034-35 (9th Cir.1997) (counsel was not ineffective at the penalty phase for failing to develop and use psychological evidence because, inter alia, the defendant’s personal' wish that “he did not want to undergo a psychological examination” was “entitled to respect”). A defendant’s insistence that counsel not call witnesses at the penalty phase does not eliminate counsel’s duty to investigate mitigating evidence or to advise the defendant of the potential consequences of failing to introduce mitigating evidence, thereby assuring that the defendant’s decision regarding such evidence is informed and knowing. See Silva, 279 F.3d at 838 (counsel rendered ineffective assistance at the penalty phase by not informing the defendant, who opposed calling certain witnesses, of the potential significance of mitigating evidence, and by not conducting any investigation of the defendant’s background). However, having reasonably investigated mitigating evidence and prepared for the penalty phase, counsel is not deficient for failing to introduce evidence in mitigation when the defendant makes an informed and knowing decision not to present the evidence. See Jeffries v. Blodgett, 5 F.3d 1180, 1197-98 (9th Cir.1993) (counsel, which had been prepared to present a mitigation case, was not ineffective for failing to present mitigating evidence when the defendant made a considered decision not to introduce evidence in mitigation). Counsel also cannot be faulted for deferring to. the defendant’s desire to forgo presentation of mitigating evidence when the defendant’s wish coincides with counsel’s reasonable professional judgment that no mitigating evidence be introduced. Campbell, 829 F.2d at 1462 n. 5, 1463 (counsel’s acceptance of the defendant’s decision not to present mitigating evidence did not constitute ineffective assistance when counsel had legitimate strategic reasons for not presenting the evidence).

In the instant case, Ingber appropriately considered Williams’s desire that no witnesses be called in making the ultimate decision not to present any evidence in mitigation. As already discussed, Ingber reasonably investigated mitigating evi *623 dence in preparation for the penalty phase. See Silva, 279 F.3d at 838 (the defendant’s directive that counsel not call particular witnesses did not extinguish counsel’s duty to investigate the defendant’s personal history in order to ascertain mitigating evidence). Moreover, the trial record shows that Ingber had witnesses that would have testified at the penalty phase if he, in consultation with Williams, decided to introduce mitigating evidence. At the same time that Ingber brought to the trial court’s attention Williams’s insistence that no witnesses testify, Ingber informed the court that defense witnesses were available to testify that day if necessary. Ing-ber also notified the court that if the defense were to put on mitigating evidence, he would seek a continuance so that he might call other witnesses whom he was unable to reach between the Friday on which the jury returned its verdict in the guilt phase and the following Tuesday on which the penalty phase was scheduled to begin. Thus, although Ingber could not recall at the federal evidentiary hearing who, besides Williams’s mother and stepfather, these defense witnesses were due to the loss of his original trial file and the passage of seventeen years, it is apparent from the trial record that Ingber was prepared to go forward with a mitigation case if he determined that was the most prudent course of action. See Jeffries, 5 F.3d at 1197-98 (although the defendant ultimately asked counsel not to introduce evidence in mitigation, counsel was prepared to present a mitigation case).

In conferring with Williams about calling witnesses at the penalty phase, Ingber adequately informed Williams of the potential ramifications of failing to present evidence in mitigation. See Silva, 279 F.3d at 838 (competent counsel must advise the defendant of the potential consequences of a decision not to introduce mitigating evidence). Ingber advised Williams that the purpose of mitigating evidence was to influence the jury to return a sentence of life imprisonment rather than the death penalty, and Ingber discussed with Williams what mitigating evidence might be presented. Ingber had no doubt that Williams fully understood the potential consequences of his wish that no witnesses testify at the penalty phase. The trial judge also impressed upon Williams the importance of presenting mitigating evidence. Williams therefore made an informed and knowing decision to forgo evidence in mitigation at the penalty phase. See Jeffries, 5 F.3d at 1198 (the defendant’s decision not to introduce mitigating evidence was informed and knowing when counsel had discussed with him the ramifications of failing to present the evidence and he appeared to understand them).

Williams’s request that no witnesses testify also coincided with Ingber’s reasonable professional judgment that introducing mitigating evidence was unlikely to help Williams much, and would probably harm him by allowing the prosecutor to present damaging rebuttal evidence of Williams’s gang activities. Accordingly, the deference that Ingber showed Williams’s request is beyond criticism. See Campbell, 829 F.2d at 1462 n. 5, 1463 (counsel reasonably deferred to the defendant’s wish that no witnesses be called when that wish was in accord with counsel’s reasonable strategic decision not to present mitigating evidence). “Counsel’s actions are usually based, quite properly, on informed strategic choices made by the defendant and on information supplied by the defendant.” Strickland, 466 U.S. at 691, 104 S.Ct. 2052. Ingber reasonably factored Williams’s wishes into the balance of considerations that ultimately persuaded Ingber not to introduce evidence in mitigation at the penalty phase.

*624 (d) Lingering Doubt Regarding Williams’s Guilt Was A Viable Defense.

Finally, Ingber reasonably selected a lingering-doubt defense for the penalty phase. As already touched upon, the prosecution’s case lent itself to such a defense because the case comprised of circumstantial evidence and the testimony of witnesses with less-than-clean backgrounds and incentives to lie in order to obtain leniency from the state in either charging or sentencing. No eyewitness linked Williams to the Brookhaven Motel robbery and murders, and the credibility of the sole eyewitness to the 7-Eleven robbery and murder, Alfred Coward, was suspect because he was an accomplice that received government immunity in exchange for his testimony against Williams. Ingber therefore could persuasively argue that lingering doubt about Williams’s guilt counseled against a death-penalty verdict. Furthermore, the lingering-doubt defense offered strategic advantages. Pursuing the defense did not require introduction of mitigating evidence that would open the door to damaging rebuttal evidence of Williams’s gang activities. In choosing the defense, Ingber also avoided conflict with Williams by respecting Williams’s request that no witnesses testify at the penalty phase.

In sum, based upon our review of the reasons underlying Ingber’s penalty-phase strategy, we cannot fault Ingber’s sound tactical decision to present a lingering-doubt defense in lieu of a defense based upon mitigating evidence of Williams’s family and life history, drug use, or mental state. We note in this regard that the defense of “ ‘residual doubt has been recognized as an extremely effective argument for defendants in capital cases.’ ” Lockhart v. McCree, 476 U.S. 162, 181, 106 S.Ct. 1758, 90 L.Ed.2d 137 (1986) (quoting Grigsby v. Mabry, 758 F.2d 226, 248 (8th Cir.1985) (en banc) (Gibson, J., dissenting)). A comprehensive study on the opinions of jurors in capital cases concluded:

“Residual doubt” over the defendant’s guilt is the most powerful “mitigating fact.” ... [T]he best thing a capital defendant can do'to improve his chances of receiving a life sentence has nothing to do with mitigating evidence strictly speaking. The best thing he can do, all else being equal, is to raise doubt about his guilt.

Stephen P. Garvey, Aggravation and Mitigation in Capital Cases: What Do Jurors Think?, 98 Colum. L. Rev. 1538, 1563 (1998) (footnote omitted); accord William S. Geimer & Jonathan Amsterdam, Why Jurors Vote Life or Death: Operative Factors in Ten Florida Death Penalty Cases, 15 AM. J. Crim. L. 1, 28 (1988) (“The existence of some degree of doubt about the guilt of the accused was the most often recurring explanatory factor in the life recommendation cases studied.”). We conclude that Ingber performed capably at the penalty phase. Accordingly, we affirm the district court’s denial of Williams’s penalty-phase claim of ineffective assistance of counsel. 22

B. Tainted Jury. (Claim Y)

Williams contends that he was deprived of his Sixth Amendment right to a fair trial and an impartial jury at the penalty phase of the trial, because of the possibility that the jury may have considered extraneous evidence at that phase of the trial. The jury rendered its verdict at the conclusion of the guilt phase on a Friday. The penalty phase of the trial began the following Tuesday. On the day *625 the jury began its penalty phase deliberations an alternate juror told the bailiff that some of the jurors believed that Williams had threatened the jury. The bailiff reported this to the judge. The judge then questioned the alternate juror in open court outside the presence of the jury. At first the judge thought that the possible threat had been made to her on Tuesday. Then it was cleared up that she was referring to something that occurred on Friday. The transcript of the questioning after that of the alternate juror, Mrs. Bela, is as follows:

THE COURT: What comment is this that you’re referring to?

MRS. BELA: It was after the verdict was read.

THE COURT: What did you hear, if anything?

MRS. BELA: Well, the jurors sitting in the center said that the defendant looked at us and said that he was going to get all of us.

THE COURT: Did you hear him say that?

MRS. BELA: No, I didn’t.

THE COURT: All right.

You may step down.

Thank you.

ER aL1954.

Williams’s co-counsel, Mr. Ehrlich, stated his belief that the comment referred to must have been one addressed to him and not the jury. Mr. Ehrlich stated:

Mr. Williams, turned to me and addressed a comment to me as his counsel. There is no — I don’t want to put myself in the position of a witness — but I think the representation should be clear that it was something to the effect, “Are those the sons of bitches who are going to decide what happens to me?”

There was no threat. Nothing directed to any juror.

It was a comment directed strictly to counsel.

ER 1956. As to what should be done at that point Mr. Ehrlich stated “It should be considered by the court as to what remedy if anything is appropriate.... [T]he court perhaps should consider inquiring as to the regular panel, perhaps declaring a mistrial as to the penalty phase.” After discussing the matter with the prosecution and defense attorneys the court decided to bring the foreman of the jury into the courtroom for questioning. The transcript of that questioning is as follows:

THE COURT: Are you the foreman during the penalty phase of this case?

MR. BRAMHALL: I am.

THE COURT: It has come to the court’s attentions that there is a possibility that some remark might have been made by the defendant that was heard by the jury on the date that the jury returned its verdict at the guilty phase. Do you have any information concerning that?

MR. BRAMHALL: Ido.

THE COURT: What is that?

MR. BRAMHALL: He did utter a statement as we were concluding.

THE COURT: What was the statement?

MR. BRAMHALL: “I’m going to get each and every one of you mother fuckers.”

THE COURT: Did you personally hear him make that statement?

MR. BRAMHALL: I did not.

I saw him mouthing it; but I did not hear it.

THE COURT: In other words, were you able to make out the words?

MR. BRAMHALL: I was not. One of the other jurors was.

THE COURT: All right.

*626 Did that play any part in the deliberations of this case concerning the penalty?

MR. BRAMHALL: It did not.

THE COURT: Was there any discussion of that comment at any time during the penalty phase of this trial?

MR. BRAMHALL: No. Not until after the verdict had been reached.

THE COURT: You’ve now reached a verdict?

MR. BRAMHALL: We have.

THE COURT: All right.

Thank you.

You may go back into the jury room.

ER at 1959-60.

It is apparent that the perceived threat to the jury was not the Williams statement to counsel, but rather one mouthed directly to the jury. This corresponds to the comment described by Foreman Bramhall. It does not correspond to the comment described by Williams’s counsel. The transcript reveals that Williams’s counsel realized this. After the penalty verdict was rendered he asked:

MR. EHRLICH: Your Honor, before you let the jury go, I wonder, Your Honor — I think the defense would request in this instance as to the comment that Mr. Bramhall recited, that perhaps the court should make inquiry of each of the twelve regular jurors individually out of the presence of the others and ask each juror specifically whether the comment was directed to him.

This isn’t a comment that apparently the court reporter got. 23 This is supposedly a mouthed threat.

ER at 1964. Williams’s counsel did not move for a mistrial, but he did request that each of the regular jurors be questioned. The court declined to do so stating, “The foreman said the matter was not discussed until after the verdict was rendered. I am willing to accept his word for it. Further, on the fact that if anything occurred, it was the defendant personally that did it.” The court had earlier expressed that misconduct of the defendant in the courtroom during official courtroom procedures and perceived by the jury was entirely different from activity or conversations that occurred outside the courtroom and were brought into jury deliberations.

The transcript of the trial makes it clear that it was the perceived direct threat to the jury that was at issue, not any statement by Williams to his counsel as earlier thought by counsel Ehrlich. Some of the jurors observed a direct threat to the jurors mouthed by Williams. This was misconduct by Williams in the courtroom during regular proceedings. It was not extraneous evidence outside the courtroom improperly brought into the jury room.

“The Sixth Amendment right to a jury trial ‘guarantees to the criminally accused a fair trial by a panel of impartial, indifferent jurors.’ ” United States v. Sarkisian, 197 F.3d 966, 981 (9th Cir.1999) (quoting Irvin v. Dowd, 366 U.S. 717, 722, 81 S.Ct. 1639, 6 L.Ed.2d 751 (1961)) (internal quotations omitted). However, the constitutional right to an impartial jury is not absolute. The Sixth Amendment affords no relief when the defendant’s own misconduct caused the alleged juror partiality and the trial judge employed reasonable means under the circumstances to preserve the trial’s fairness. See United States v. Hernandez, 952 F.2d 1110, 1116—18 (9th Cir.1991) (no relief when a juror *627 observed the defendant making “a slit across his throat, a motion to the witness who was on the stand” and the court questioned the juror and admonished the entire jury to ignore any gestures or body language); United States v. Trevino-Rodriguez, 994 F.2d 533, 535 (8th Cir.1993)(no relief when the defendant interrupted defense counsel’s opening statement and the trial court called an immediate recess, excused the jury, and the trial judge gave a curative instruction when the jury returned); United States v. Chaussee, 536 F.2d 637, 639-41 (7th Cir.1976) (no relief when the defendant attempted to escape from the courtroom in the jury’s presence and the trial judge fully informed himself of what had occurred, assessed its impact on the jury, and promptly admonished the jury to disregard the defendant’s misconduct), abrogated on other grounds by Lewis v. United States, 523 U.S. 155, 162, 118 S.Ct. 1135, 140 L.Ed.2d 271 (1998); see also Illinois v. Allen, 397 U.S. 337, 346, 90 S.Ct. 1057, 25 L.Ed.2d 353 (1970) (the defendant’s Sixth Amendment right to be present in the courtroom at every stage of trial is not absolute and may be lost by the defendant’s misconduct).

Our decision derives from practical concerns about the proper administration of criminal justice, which would suffer appreciably if defendants through their own misconduct could overturn the results of their trials. “[Granting [habeas corpus relief] on the basis of [the defendant’s] own misconduct would subvert the judicial process and allow [the defendant] to benefit from his own wrongdoing. If such behavior on the part of the defendant were held to require [relief], ‘it would provide an easy device for defendants to provoke [constitutional error] whenever they might choose to do so.’ ” United States v. Stewart, 256 F.3d 231, 242 (4th Cir.2001) (quoting United States v. West, 877 F.2d 281, 289 (4th Cir.1989)). Justice Brennan, in his concurring opinion in Allen, 397 U.S. at 349, 90 S.Ct. 1057 (quoting Falk v. United States, 15 App.D.C. 446 (1899)), recognized this problem:

It does not seem ... to be consonant with the dictates of common sense that an accused person ... should be at liberty, whenever he pleased, ... to break up a trial already commenced. The practical result of such a proposition, if allowed to be law, would be to prevent any trial whatever until the accused person himself should be pleased to permit it ... This would be a travesty of justice which could not be tolerated.... Neither in criminal nor in civil cases will the law allow a person to take advantage of his own wrong.

Nonetheless, even when it is the defendant’s own misconduct that jeopardizes the fairness of the trial, the trial court must use reasonable means tailored to the particular circumstances of the case to help ensure a fair trial. See Chaussee, 536 F.2d at 641.

In this case any curative instruction would have stated that any mouthed threat that any jurors observed should play no part in the jury’s deliberations. The foreman had already stated that it was not discussed in the jury’s deliberations. There would have been no purpose for such an instruction at that point.

It is clear that it was Williams’s mouthed threat that created any possible problem in this regard, thus invoking the strong policy that a defendant should not profit from his own wrongdoing at trial. Furthermore, as concluded by the California Supreme Court, the trial judge’s actions were reasonable to ensure that the jurors considered the case on the evidence presented, unaffected by any threat perceived from Williams’s statement. The judge had earlier instructed the jurors *628 that they must base their verdicts upon evidence, and “evidence is what [they] heard from the witness stand and exhibits that were introduced into evidence.” Prior to receiving the jurors’ verdicts the judge informed himself of what had occurred and determined that the jury had not discussed any perceived threat by Williams during the jurors’ deliberations. In light of the strong policy against a defendant profiting from his own wrongdoing at trial and the trial judge’s reasonable actions to ensure a fair trial, we conclude that Williams is not entitled to relief under the Sixth Amendment, and we affirm the district court’s grant of summary judgment in the state’s favor on this claim.

CONCLUSION

Finding no constitutional basis to disturb Williams’s 1981 conviction or death sentence, we affirm the district court’s judgment denying Williams’s habeas corpus petition. We also vacate the district court’s order denying Williams’s Rule 60(b) motion because the district court lacked jurisdiction to consider the motion. With these holdings, we necessarily conclude that Williams is not entitled to relief from his conviction or sentence in the federal courts. We note, however, that the federal courts are not the only forum for relief, and that Williams may file a petition for clemency with the Governor of California. See CAL. CONST, art. V, § 8. We are aware of Williams’s 2001 Nobel Peace Prize nomination for his laudable efforts opposing gang violence from his prison cell, notably his line of children’s books, subtitled “Tookie Speaks Out Against Gang Violence,” and his creation of the Internet Project for Street Peace. See generally Tookie’s Comer, at http://www.tookie.com (last modified Feb. 28, 2002). Although Williams’s good works and accomplishments since incarceration may make him a worthy candidate for the exercise of gubernatorial discretion, they are not matters that we in the federal judiciary are at liberty to take into consideration in our review of Williams’s habeas corpus petition. We affirm the district court’s judgment denying Williams’s habe-as corpus petition and vacate the district court’s order denying Williams’s Rule 60(b) motion.

AFFIRMED IN PART AND VACATED IN PART.

. The California Supreme Court and the district court erroneously referred to the victim as Alvin Owens. See Williams I, 245 Cal. Rptr. 635, 751 P.2d at 905; Williams v. Calderon, 48 F.Supp.2d 979, 986 (C.D.Cal.1998).

. James Garrett also provided testimony linking Williams to the 7-Eleven murder. Ac *580 cording to Garrett, Williams admitted that he had killed a white man in a store by shooting him in the head with a shotgun while the man was on his hands and knees. See Williams I, 245 Cal.Rptr. 635, 751 P.2d at 906 n. 4.

. The state had dismissed the third count of armed robbery and the kidnapping count" on February 25, 1981.

. The COA does not reach issues raised by the district court's denial of Williams's motion to amend under Rules 52(b) and 59(e). Although Williams filed an amended notice of appeal indicating his intent to appeal the district court’s denial of his motion to amend, Williams does not raise any challenge to this denial in his briefs on appeal. Williams “has abandoned those claims that he does not address in his briefs.” Morris, 229 F.3d at 779. Thus, we do not grant a COA on these issues and lack jurisdiction to consider them. See 28 U.S.C. § 2253(c).

. The state argues that Williams waived his excessive security claim on appeal because his discussion of the claim in his opening brief is limited to a footnote. We disagree. In assessing whether an issue is sufficiently argued to avoid waiver, we look at whether the opening brief contains the appellant’s contentions as well as citations to authorities and the record. See Fed. R.App. P. 28(a)(9)(A) (the argument in appellant's opening brief must contain “appellant’s contentions and the reasons for them, with citations to the authorities and parts of the record on which the appellant relies”); Nat'l Ass’n for the Advancement of Psychoanalysis v. California Bd. of Psychology, 228 F.3d 1043, 1049 n. 3 (9th Cir.2000) (an issue is waived if the brief does not contain the appellant’s contentions and citations to authorities and the record). We conclude that Williams's argument, consisting of eight sentences in a footnote in his opening brief, preserved his excessive security claim for appellate review. The argument identifies the basis of Williams’s disagreement with the district court's ruling and his requested relief from this court. The argument also contains supporting citations to case law and the record. Although not extensive, Williams's argument is more than the "summary mention of an issue in a footnote, without reasoning in support of the ... argument.” Hilao v. Marcos, 103 F.3d 767, 778 n. 4 (9th Cir.1996) (declining to consider the issue). We therefore consider the merits of Williams's excessive security claim.

. In its supplemental briefing filed with this court, the state argues that Williams waived the merits of his shackling claim, requesting only that we remand for an evidentiary hearing on the claim. We disagree. Williams’s opening brief disputes the district court’s factual findings, which the state itself noted in its earlier-filed answering brief, and also the merits of the court’s ultimate holding of harmless error based upon these findings. See Williams IV, 41 F.Supp.2d at 1047-48 (concluding that Williams's physical restraints were harmless error because Williams was not handcuffed in the courtroom, only one juror saw Williams in handcuffs going to or from court, and no juror viewed Williams’s leg chain in the courtroom). Williams has therefore properly preserved for appellate review the merits of his shackling claim, which we consider below. See Jones v. Wood, 207 F.3d 557, 562 n. 2 (9th Cir.2000).

. The state, however, had not charged Coleman with any of the crimes of Williams's case.

. Because we affirm on the ground that the trial court’s admission of Coleman’s testimony was not constitutional error, we do not reach the district court’s alternative holding that any error was harmless. See Williams III, 48 F.Supp.2d at 1001-02.

. In his briefs, Williams represents his claim as challenging the prosecution's failure to disclose an agreement for the testimony of both James and Esther Garrett. However, in his amended habeas corpus petition filed with the district court, Williams complained of an undisclosed, prosecutorial deal with only James Garrett. Moreover, in ruling on this claim, the district court addressed the merits of the alleged agreement with James Garrett, and *597 did not consider any agreement with Esther Garrett. See Williams III, 48 F.Supp.2d at 1002-03. Thus, the issue of an undisclosed, prosecutorial deal with Esther Garrett is not properly before this court. See Ecological Rights Found. v. Pac. Lumber Co., 230 F.3d 1141, 1154 (9th Cir.2000) (an issue is generally waived on appeal if it is not adequately raised below to the district court). We do not consider the issue.

. Although Williams contends that the evi-dentiary hearing at which the California Supreme Court developed these factual findings was not full and fair, see 28 U.S.C. § 2254(d)(6) (West 1994), we reject this argument below and so presume the correctness of the findings regarding the 1978 tape recording. The state evidentiary hearing also precludes the possibility of a federal eviden-tiary hearing on this tape recording. See Phillips, 267 F.3d at 973 (a habeas petitioner is not entitled to a federal evidentiary hearing if the state court trier of fact has, after a full and fair hearing, reliably found the relevant facts).

. With this assumption, we obviate any need for a federal evidentiary hearing to develop the facts of the 1979 tape recording.

. This is the same tape recording discussed above in the context of Williams’s due process claim that the prosecution improperly suppressed at trial material, exculpatory evidence impeaching Oglesby's credibility.

. We question whether White would have testified as Williams represented given the evidence that about a year before the second state hearing, White recanted his 1989 declaration, stating that it was a lie. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1091. It also appears from the state-court record that Williams failed to substantiate the testimony that his witnesses allegedly would have provided with anything more than his or his counsel’s unsupported assertions. We have previously indicated that satisfaction of the relevance prong requires the defendant to offer proof of the substance of a defense witness's testimony beyond the defendants or defense counsel’s unsupported assertions. See Westerdahl, 945 F.2d at 1086; Prantil v. State of Cal., 843 F.2d 314, 318 (9th Cir.1988). Nonetheless, because we dispose of Williams's second argument under the prose-cutorial misconduct prong, we assume that he has sustained his burden of proof on the relevance prong.

. We do not reach the merits of Williams's claim that the admission of Oglesby’s testimony violated the Sixth Amendment right to counsel because Williams does not challenge this aspect of the district court’s decision on appeal. See Laboa, 224 F.3d at 981 n. 6 (issues not specifically and distinctly argued in the appellant’s opening brief are waived on appeal).

. We reject the state’s contention that Williams waived the merits of both of these claims regarding his incompetence at trial. See Jones, 207 F.3d at 562 n. 2 (the appellant's failure to argue an issue in the opening brief constitutes waiver of the issue on appeal). In his opening brief, Williams sufficiently argued the merits to avoid waiver on appeal.

. The trial judge also issued an order that Dr. Ronald Siegel examine Williams. However, Dr. Siegel’s report in the record is addressed to defense counsel. Because the record does not make clear whether the trial judge ever received a copy of Dr. Siegel’s report, we do not consider it in our analysis of Williams’s procedural-due-process claim. See Lewis, 991 F.2d at 527 (in reviewing whether a state trial judge should have sua sponte conducted a competency hearing, a federal court may consider only the evidence that was before the trial judge). In any event, Dr. Siegel’s conclusions are consistent with those reached by Drs. Coodley and Coburn. Thus, even if we did consider Dr. Siegel's report, it would not alter our analysis of Williams's claim.

. We therefore do not reach Williams's claim that he is entitled to an evidentiary hearing on the issue of the prejudice he suffered from defense counsel’s ineffective assistance at the guilt phase. Because we do not remand, we decline Williams’s request that we instruct the district court to consider on remand the opinion of his Strickland expert. In any event, the district court’s decision not to admit this expert testimony was not prejudicial abuse of discretion. See United States v. Hankey, 203 F.3d 1160, 1166-67 (9th Cir.2000).

. It appears that much of Ingber’s original trial file was misplaced as it changed hands from Ingber to Williams’s counsel in the state habeas corpus proceedings, and then to Williams’s counsel in the present federal ha-beas corpus proceedings.

. Although a second attorney, Steve Ehrlich, was Ingber’s co-counsel at Williams's trial, Ingber was lead counsel with full responsibility for the trial. We focus on Ingber’s representation because all of the evidence adduced with respect to Williams’s ineffective-assistance-of-counsel claims relates to Ingber's investigation and decision making.

. Williams argues that Ingber did not review Dr. Siegel's report, relying upon Ingber’s statement at the federal evidentiary hearing, held seventeen years after trial, that he had no independent recollection of the report. However, the district court found that Ingber saw and considered Dr. Siegel's report in preparing for trial based upon evidence that the report was in the case file given to Ingber by earlier counsel. See Williams IV, 41 F.Supp.2d at 1051. Given Ingber’s statement at the 1985 evidentiary hearing, conducted in conjunction with the state habeas corpus proceedings, that he reviewed all documents transferred to him from prior counsel in preparing for Williams's trial, the district court's factual finding that Ingber saw and considered Dr. Siegel's report is not clearly erroneous.

.By the time of Williams's trial, Ingber's experience was significant. At that point, Ingber had been practicing criminal law for twenty years, and had handled at least forty special-circumstance murder cases, about half of which went to trial.

. We do- not reach Williams’s claim that the district court erred in its alternative holding that Williams suffered no prejudice from Ing-ber’s performance at the penalty phase.

. The reporter had picked up the words "sons of bitches” from the comment Williams made to his counsel. There is no indication the jury heard those words.