Robert Carter appeals the denial of his petition for a writ of habeas corpus filed under 28 U.S.C. § 2254 (1996). We affirm the judgment and vacate the stay of execution.
I.
Carter was convicted of capital murder and sentenced to death in March 1982. His case, *456 which languished in the Texas courts for over a decade and recently reached the Supreme Court, has now been remanded to this court for further action.
A.
Carter was arrested in 1981 and charged with the murder of Sylvia Reyes, who was fatally wounded during the robbery of a service station. 1 Carter confessed in great detail to the murder but stated that the shooting had been accidental and denied any intent to kill Reyes. Pursuant to this confession, the police obtained the murder weapon identified by Carter, and ballistic experts confirmed that the revolver had been used in the murder.
B.
At trial, a witness identified as “David Josa” testified that he was entering the service station when he heard gunshots inside and observed two individuals leave it immediately thereafter. The first fled but returned when the police arrived. The second, a young black man fitting Carter’s description, emerged from the store with “a wad of money” in his left hand and fled. Josa observed this person for only a few seconds but did not see a gun, nor was he able subsequently to identify Carter as the second man.
Another witness, Arthur Mallard, corroborated Josa’s testimony. Mallard identified himself as the first person out of the station and testified that he had observed a man fitting Carter’s description reach across the counter to take money from the cash register. When the station attendant resisted, Mallard heard a gunshot and fled the store. He was unable to identify Carter as the man he had seen.
The defense offered no evidence to rebut the state, and the jury returned a verdict of guilty to capital murder. At the penalty stage, the state called witnesses to establish that Carter had committed another murder six days prior to the charged offense. Although none of the witnesses directly observed the second murder, one identified Carter as the man she observed fleeing the scene. Finally, the state introduced Carter’s confession, in which he confessed to the second murder, once again.
In rebuttal, defense counsel offered the testimony of three witnesses — Carter, his mother, and a family friend — to establish Carter’s good character. Carter testified that he had not intentionally killed the two •victims and pledged to rehabilitate himself if sentenced to life imprisonment rather than death. Finally, in response to the character evidence, detective L.B. Smith testified that Carter’s reputation as a peaceful and law-abiding citizen was “bad.” After brief deliberation, the jury affirmatively answered the three special issues submitted pursuant to Tex.Code CRiM.PROC.ANN. art. 37.071 (Vernon 1981), and the trial court imposed the death sentence.
C.
In 1990, Carter filed his first state habeas petition. In August 1995, the state trial court recommended that state habeas relief be denied, and the Texas Court of Criminal Appeals denied this first habeas petition in December 1995.
In August 1995, while the original state habeas petition was pending, Carter filed his second state habeas application, alleging that the length of time between his sentencing and his scheduled execution rendered his death sentence cruel and unusual punishment in violation of the Eighth Amendment. The state trial court recommended that habeas relief be denied, and the Court of Criminal Appeals denied this second application in January 1996.
Having finally exhausted his state remedies, Carter filed the instant federal habeas petition in January 1996, followed soon thereafter by a motion for discovery, a motion for an evidentiary hearing, and an application for stay of execution. On March 20, 1996, the federal district court entered final judgment, denying habeas relief. Carter appealed, and *457 the district court issued a certificate of probable cause (“CPC”) on April 19,1996.
We affirmed on April 9, 1997.
See Carter v. Johnson,
II.
A.
Our initial opinion,
In our initial opinion, we held that the AEDPA’s procedural provisions could be applied to Carter’s habeas petition despite the fact that his case was initiated before the effective date.
Carter,
B.
Before reaching the merits, we must decide whether we have jurisdiction to entertain the appeal. Although neither party has challenged our jurisdiction, we are obliged to raise the issue sua sponte. 4
The AEDPA became effective April 24, 1996, five days after Carter’s CPC was issued. Under similar circumstances, we recently held that the AEDPA’s requirement of a COA does not apply to habeas applicants who obtained CPC’s prior to the statute’s effective date.
See Brown v. Cain,
III.
When we initially decided this case, we followed
Drinkard v. Johnson,
IV.
Carter alleges that the state introduced the fraudulent testimony of an “imposter witness” at trial, thereby incriminating him and undermining the integrity of the verdict. To succeed on such a claim, Carter must establish three elements: first, that false testimony was presented at trial; second, that the prosecution had actual knowledge that the testimony was false; and third, that the testimony was material.
May v. Collins,
A.
The sole evidence Carter offers to establish the first element is the affidavit of David Josza. Josza, who was identified as an eyewitness during the murder investigation, avers that he did not testify at Carter’s trial. Nevertheless, the trial transcript indicates that an individual identified as “David Josa” testified for the prosecution, offering substantially the same testimony as the statement given by Josza during the investigation. Therefore, Carter concludes that the witness who testified at trial must have been an imposter. Even if we assume, arguendo, that the testimony was fraudulent, the introduction of fraudulent testimony is insufficient by itself to entitle Carter to habeas relief. 6
B.
The Fourteenth Amendment is implicated by the introduction of fraudulent or perjured testimony only if the prosecution has actual knowledge of the perjury.
7
We have consistently stated that this requirement imposes a strict burden of proof on a federal habeas petitioner.
See, e.g., May,
Carter relies exclusively on circumstance and inference, arguing that an “imposter witness” could not possibly testify at trial without the substantial complicity of the prosecution. To rebut this inference, the state introduced the affidavit of then-prosecutor Brian Rains, which the state court found to be credible, averring that he would not knowingly or intentionally present an imposter witness at trial. After weighing this competing evidence, the state court concluded there was no evidence that the state had knowingly or intentionally presented an “imposter witness” at trial.
These factual findings are entitled to a presumption of correctness. 8 The state court reasonably determined that Carter had not satisfied his burden to prove that the prosecution knowingly or intentionally presented perjured testimony at trial. We have no reason to doubt either the fairness of the state court’s procedure or the correctness of its result.
*459 C.
Both the state habeas court and the federal district court dismissed the perjury-claim on the ground that the alleged perjury was not material to the outcome of the trial. For the perjury to be material, Carter must show that “there was any reasonable likelihood that the false testimony could have affected the judgment of the jury.” 9 Under the circumstances of this case, Carter cannot make such a showing.
Given that the star witness for the prosecution was Carter, whose confession was introduced into evidence, there is no reasonable likelihood that Josa’s allegedly. false testimony affected the verdict. The prosecution did not rely on Josa’s testimony to establish the essential elements of the offense, but merely to corroborate the confession. Moreover, the contested evidence was cumulative of other evidence, particularly Mallard’s testimony.
Carter has failed to establish that the prosecution knowingly and intentionally presented material false evidence. Accordingly, we find no error in the state court’s determination on this issue.
V.
Carter contends that the district court erred by failing to conduct a nunc pro tunc evidentiary hearing to determine his competency to stand trial. We disagree.
A.
The trial and conviction of a defendant while he is mentally incompetent constitute a denial of due process.
See Cooper v. Oklahoma,
*460
A habeas petitioner is entitled to a
nunc pro tunc
evidentiary hearing for the purpose of proving that he was incompetent at the time of trial only “when he makes a showing by clear and convincing evidence to raise threshold doubt about his competency.”
Lokos v. Capps,
Both the state habeas court and the federal district court concluded that a nunc pro tunc evidentiary hearing was not required to decide whether Carter was incompetent at trial. Indeed, the state habeas court expressly concluded that Carter was competent: “The Court finds that the applicant’s testimony during the punishment stage of the trial shows a factual, as well as rational understanding of the proceedings against him.” Moreover, the state habeas court entered the following conclusion: “The applicant fails to show that he was legally incompetent to stand trial, i.e., that he was unable to consult with .counsel with a reasonable degree of rational understanding or that he lacked a factual, as well as rational, understanding of the proceedings against him.” These findings are more than adequate to justify the district court’s conclusion that “the state court found that there was no evidence that Petitioner was actually incompetent to stand trial.” 12
Under 28 U.S.C. § 2254(d), the findings are entitled to a presumption of correctness. . The petitioner must rebut this presumption by clear and convincing evidence, and a federal court may not issue a writ unless the petitioner can demonstrate by such evidence that the state decision was based on an incorrect determination of the facts. Furthermore, the factual determination of the state habeas court, finding that Carter failed to establish he was legally incompetent to stand trial, must be afforded the presumption of correctness. 13
*461 B.
Given the combined weight of the presumption of correctness and the high burden of proof necessary to justify a nunc pro tunc evidentiary hearing on the question of competency, Carter has failed to demonstrate that the state habeas court erred in denying his allegation of incompetency. Carter relies primarily on the affidavit of Dr. Dorothy Lewis, his board-certified psychiatrist, who concluded that a history of head injuries, mental retardation, and brain damage impaired his ability to make mature judgments, appreciate the consequences of his behavior, and reflect in advance on the appropriateness of his actions. The fact that neither the state habeas court nor the district court discussed this expert opinion does not overcome the presumption of correctness.
First, Lewis did not offer her opinion that Carter was unable to consult with his lawyers with a reasonable degree of rational understanding or was unable to command a rational or factual understanding of the proceedings against him — the minimum standard for a finding that he was incompetent. Therefore, it was not unreasonable for the state habeas court to find this expert testimony-unpersuasive.
Furthermore, the state habeas court is entitled to find a defendant competent, despite the introduction of psychiatric testimony diagnosing him as incompetent, without ordering an evidentiary hearing.
See, e.g., Maggio,
To the contrary, the state habeas court expressly found that Carter’s testimony established that he possessed a rational and factual understanding of the proceedings against him. Such a conclusion by a state court, based upon a defendant’s testimony, is entitled to a presumption of correctness.
See Holmes v. King,
Finally, Carter corroborates his claim of incompetency with evidence of physical abuse and neglect and with anecdotal comments made by the prosecutor and defense counsel at trial. Nevertheless, the state habeas court found credible and persuasive the affidavits offered by Carter’s court-appointed trial counsel, who stated that they believed he was competent to stand trial and did not think his prior head injuries had impaired his mental competency during the trial. These factual findings are entitled to the presumption of correctness, and the anecdotal evidence is insufficient to overcome this presumption by clear and convincing evidence.
VI.
Carter did not contest the voluntariness of his confession, and it thus was admitted into evidence without objection. Nevertheless, he now collaterally attacks the admissibility of the confession on the ground that it was involuntary. His claim is meritless.
A.
A federal court entertaining a collateral challenge to the voluntariness of a confession is obliged to afford a presumption of correctness to state court findings of fact if fairly supported in the record but is authorized to exercise de novo review over the ultimate conclusion of whether, under the *462 totality of the circumstances, the confession was “voluntary.” 14
B.
Pursuant to
Jackson v. Denno,
Likewise, the state habeas court entered extensive factual findings concerning the vol-untariness of the confession, finding, inter alia, that Carter was timely advised of his Miranda rights; that he understood his rights, yet declined to request the presence of either an attorney or a family member while in custody; that he was offered no inducements to confess and suffered no threats or coercion to extract a confession while in custody; that he was mentally competent and cooperative at the time he made his confession; and that he acknowledged that his statement was made voluntarily. These factual findings are entitled to the presumption of correctness under 28 U.S.C. 2254(d) (1988). To overcome the presumption, Carter must rebut these factual findings by clear and convincing evidence. Id. This he cannot do.
In his federal habeas petition, Carter sought to overcome the factual findings by raising charges of coercion, intimidation, and mental retardation. The district court found, however, that his allegations of coercion and duress were conelusional and unsupported by the evidence adduced at trial or presented by affidavit, and likewise found that the allegation of mental retardation was without merit. This factual determination is adequately supported by the record. Therefore, we must accept as conclusive the state court factual determination that the challenged confession was given voluntarily, not as a product of coercion or intimidation.
C.
Accepting these subsidiary facts as true, we must reach the ultimate question whether Carter’s challenged confession was voluntary or constitutionally infirm. The state trial and habeas courts concluded that it was voluntary. Applying pre-AEDPA law, the ultimate question whether a confession is voluntary is a question of law, to be reviewed
de novo. See United States v. Scurlock,
Coercive police conduct is a necessary prerequisite to the conclusion that a confession was involuntary, and the defendant must establish a causal link between the coercive conduct and the confession.
See Colorado v. Connelly,
VII.
Carter raises a litany of ineffective-assistance-of-eounsel claims, urging that his court-appointed trial counsel were constitutionally defective at both the guilt and punishment stages of the trial. Carter is unable, however, to overcome the rigorous burden of proof required to demonstrate ineffective assistance.
A.
A habeas petitioner alleging ineffective assistance must demonstrate both constitutionally deficient performance by counsel and actual prejudice as a result of such ineffective assistance.
See Strickland v. Washington,
To establish deficient performance, the petitioner must prove that the performance of counsel fell below an objective standard of reasonableness.
Id.
at 688,
Moreover, even if counsel’s performance was deficient, Carter must affirmatively demonstrate actual prejudice. To do so, he must establish that the attorneys’ errors were so deficient as to render the verdict fundamentally unfair or unreliable.
See Lockhart v. Fretwell,
For purposes of federal habeas review, state court findings of fact made in the course of deciding an ineffectiveness claim are entitled to a presumption of correctness.
See
28 U.S.C. § 2254(d) (1988);
see also Washington,
The ultimate determination whether counsel was constitutionally ineffective is a mixed question of law and fact that federal habeas courts have traditionally reviewed
de novo. See, e.g., Salazar v. Johnson,
B.
1.
Carter avers that his trial counsel were ineffective because they failed to challenge his competency to stand trial. The state habeas court, however, accorded credibility to counsel’s affidavits, averring that they had no reason to believe that Carter was mentally incompetent at the time of trial. Furthermore, the state habeas court found there was *464 insufficient evidence to conclude that Carter was mentally incompetent.
These findings of fact and credibility determinations are entitled to a presumption of correctness, and Carter has not introduced the requisite clear and convincing evidence to prove that they are erroneous. Therefore, because the factual determination that Carter was competent to stand trial is conclusive and binding on us, it necessarily follows that his trial counsel were not constitutionally ineffective in their failure to contest the competency of the defendant to stand trial. “There can be no deficiency in failing to request, a competency hearing where there is no evidence of incompetency.”
McCoy v. Lynaugh,
2.
Carter alleges that his counsel might have exposed the alleged “imposter witness” if they had interviewed David Josza prior to trial. Carter did not raise this argument explicitly in the district court, but argues that it is subsumed within his argument that counsel were ineffective in failing to interview government witnesses and adequately to prepare for trial. This vague allegation was not sufficient to place the district court on notice of the claim that Carter now urges, however, and thus the claim is deemed abandoned. 17
Furthermore, Carter’s argument that his trial counsel “might” have exposed the alleged “imposter witness” is pure speculation, insufficient to overcome the strong presumption of competency and the high burden of actual prejudice required to prove ineffective assistance of counsel. Indeed, given that the contested testimony was merely cumulative and immaterial to the outcome of the trial, 18 we cannot conclude that there is a reasonable probability that the jury would have harbored a reasonable doubt about guilt, even if the alleged “imposter witness” had been “exposed” by trial counsel. The voluntary confession precluded any such reasonable doubt, so Carter is entitled to no relief on this claim.
3.
Carter alleges that his trial counsel were ineffective in failing to challenge the admissibility of his confession. But, as we noted previously, the state habeas court accorded credibility to counsel’s affidavits, finding that the attorneys were justified in their conclusion that the confession had been given voluntarily and that there were no grounds to object to admissibility. Moreover, both the state trial court and the state habeas court found that the confession was voluntary.
The presumption of correctness attaches to these factual findings and credibility determinations, and Carter cannot overcome it. At a minimum, we cannot conclude that the performance of counsel was “objectively unreasonable.”
See Washington,
4.
Carter claims that his trial counsel were defective in their presentation of the “accidental death” defense, whereby they argued that Carter had not actually intended to kill Reyes but had accidentally discharged the weapon during a brief struggle at the cash register. Carter contends that his counsel denigrated the “accidental death” defense during their closing arguments. Furthermore, he argues that his counsel were deficient for failing to propose a jury instruction on the question of accident. These allegations were not adequately presented to the district court, however, and they are deemed waived.
See Nichols,
5.
Carter claims that his defense counsel were deficient in failing adequately to *465 investigate the facts of the ease and Carter’s background; he claims that such an investigation would have produced numerous character witnesses who would have testified during the punishment stage of the trial, as well as expert testimony concerning his mental incápacity. Therefore, Carter contends, the deficient performance of counsel deprived him of mitigating evidence that would have significantly influenced the jury’s decision whether to impose the death penalty. The state habeas court found, however, that the testimony of such character witnesses would have been cumulative and would not have been sufficient to change the verdict. We have no reason to question this conclusion.
Given Carter’s confession to the crime of murder, we can hardly conclude that the testimony of character witnesses to his reputation as a “good and peaceful person” would have sufficiently impressed the jury to avoid the sentence of death. Consequently, the conclusion of the state habeas court that Carter failed to demonstrate prejudice resulting from the absence of such character witnesses was not error.
As to the allegation that defense counsel were deficient in their failure adequately to investigate mental capacity and to secure expert witnesses who would offer mitigating evidence at the punishment stage, that claim is foreclosed by the factual conclusion that defense counsel were justified in believing that Carter was mentally competent at the time of trial. 19 Furthermore, the state habeas court found that there was insufficient evidence to warrant the conclusion that Carter was incompetent in fact at the time of trial, necessarily foreclosing any claim of ineffective assistance predicated on the failure to investigate such alleged incompetency. See McCoy, 874 F.2d at 964.
The duty of trial counsel to investigate is tempered by the information provided to counsel by the defendant. When, as here, the defendant has given counsel reason to believe that certain investigations would be fruitless or harmful, the failure to pursue such investigations may not later be challenged as unreasonable. “In any ineffectiveness case, a particular decision not to investigate must be directly assessed for reasonableness in all the circumstances, applying a heavy measure of deference to counsel’s judgments.”
Washington,
6.
Carter argues that his defense counsel were defective in failing to object to the admissibility of-his confession to the murder of R.B. Scott, an extraneous offense that was introduced by the prosecution during the punishment stage to justify the imposition of the death penalty. Carter claims there was insufficient evidence to corroborate this confession and insists that it would have been excluded from the jury on a proper objection. Carter concedes, however, that he did not raise this issue in the .district court. Therefore, it is deemed waived.
See Nichols,
7.
Carter claims that his trial counsel were deficient in failing to instruct the jury that “deliberate” conduct requires proof of something more than “intentional” conduct under
*466
Texas law.
21
Carter failed to raise this issue before the district court, however, thereby abandoning it.
See Nichols,
8.
Carter charges that defense counsel demonstrated a personal antipathy toward him during their closing arguments in the punishment phase of the trial, thereby prejudicing the jury.
22
The state habeas court, however, summarized in great detail counsel’s closing arguments, noting that counsel pleaded for mercy and compassion, summarized the arguments against the death penalty, and urged the jury to sentence Carter to life imprisonment rather than death. Therefore, defense counsel did not abdicate their role as advocates, and the state habeas court concluded that their closing arguments did not transgress the “objective standard of reasonableness.”
Washington,
In considering whether counsel’s closing argument was ineffective, we consider the closing statements in their entirety.
Teague v. Scott,
VIII.
Carter argues that execution of his death sentence, more than fourteen years after his conviction, would violate the Eighth Amendment. We have previously held, however, that such a delay does not offend the Constitution. 24 Concluding that the district court correctly refused to issue the writ of habeas corpus, we AFFIRM the judgment and VACATE the stay of execution.
Notes
. The first opinion of the Texas Court of Criminal Appeals summarizes the facts at length.
See Carter v. State,
. The acronym “GVR” refers to the Supreme Court’s practice of granting certiorari, vacating, and remanding for further consideration in light of some intervening development. The practice is thoroughly explained in
Lawrence v. Chater,
. The AEDPA significantly altered the landscape of federal habeas corpus jurisprudence. First, it imposed a jurisdictional prerequisite on appeal from a final order in a federal habeas proceeding, prohibiting the appeal unless a circuit justice or judge issues a "certifícate of appealability” ("COA”). See AEDPA § 102 (codified at 28 U.S.C. § 2253(c)(1)). Second, the AEDPA amended the procedures governing collateral review of state convictions in federal court. See AEDPA §§ 101-106 (codified at 28 U.S.C. §§ 2241-2255). And finally, the AEDPA provides for expedited procedures governing federal habeas petitions in capital cases. See AEDPA § 107 (codified at 28 U.S.C. §§ 2261-2266).
. See, e.g., United States v. Brewer,
.
Lindh
holds that while Congress did not intend immediate application of chapter 153 of the AEDPA, it did intend immediate application of chapter 154, which provides for expedited procedures in qualifying states.
See Lindh,
521 U.S. at -,
. Concluding that it was impossible to verify die identity of the challenged witness ten years after the fact, neither the state habeas court nor the federal district court found that David Josza did actually testify at trial. Because we hold that Carter failed to establish either knowledge or prejudice, however, we need not determine whether the contested testimony indeed was fraudulent.
.
See, e.g., United States v. Agurs,
.
See
28 U.S.C. § 2254(d) (1988) (stating the presumption of correctness that was in effect before enactment of the AEDPA);
Buxton v. Lynaugh,
.
Agurs,
. The issue of competency may arise in two distinct contexts.
See United States v. Williams,
First, a habeas petitioner may allege that state procedures were inadequate to ensure that he was competent to stand trial. A trial court must conduct an inquiry into the defendant's mental capacity
sua sponte
if the evidence raises a
bona fide
doubt as to competency.
Pate v. Robinson,
If a Pate violation is established, the federal habeas court must consider whether a meaningful hearing can be held nunc pro tunc to determine retrospectively the petitioner’s competency as of the time of trial. Id. at 1262. If so, the petitioner bears the burden of proving his incompetence by a preponderance of the evidence; if not, the habeas writ must issue, subject to retrial at the state's discretion. Id. This Pate procedural guarantee is not before us, having been expressly abandoned by Carter on appeal.
Second, a habeas petitioner may collaterally attack his state conviction by directly alleging incompetence at the time of trial, thereby claiming a violation of the substantive right not to be tried and convicted while incompetent, rather than of the procedural guarantee of a competency hearing in the event that a bona fide doubt arises at trial as to competency:
It is always open for the defendant to later assert his actual incompetence at trial in a subsequent collateral proceeding, but the substantive claim should not be confused with a defendant’s procedural rights under Pate to a hearing whenever a bona fide doubt as to competence surfaces at trial.
Reese v. Wainwright, 600 F.2d 1085, 1093 (5th Cir.1979).
Although Carter originally claimed both (1) that the state trial court violated his due process rights by failing to conduct an evidentiary hearing on his competency to stand trial sua sponte and (2) that the federal district court should conduct a nunc pro tunc evidentiary hearing to determine his competency at the time of trial, he has abandoned the former claim on appeal. *460 Therefore, the issue before us is restricted to the question whether the district court erred by failing to conduct a nunc pro tunc evidentiary hearing on the question of competency at the time of trial.
.
United States v. Williams,
. Carter claims that the state habeas court entered findings of fact and conclusions of law exclusively on the procedural Pate claim, not the substantive incompetency claim, thereby forfeiting the presumption of correctness afforded state court factual findings under 28 U.S.C. § 2254(d) (1988) for the latter claim. Although the findings of fact are not exhaustive, it is significant that the findings entered by the state habeas court are not limited to the narrow' question of whether a bona fide doubt existed at trial concerning Carter's competency, but also support the conclusion that he was "competent in fact” at the time of trial.
.
See Maggio v. Fulford,
Furthermore, although our prior decisions have characteristically involved cases in which the state habeas judge was the same judge who presided at trial,
see, e.g., May,
.
Thompson v. Keohane,
.
Pemberton v. Collins,
. Consequently, Carter’s allegations concerning his state of mind at the time of the confession are unavailing, for "while mental condition is surely relevant to an individual’s susceptibility to police coercion, mere examination of the confessant's state of mind can never conclude the due process inquiry.’’
Connelly,
.
See Nichols v. Scott,
. See supra part IV.
.
See Byrne v. Butler,
. Carter pleads for an exception to this rule, claiming that a miscarriage of justice will result from our refusal to address his argument. This claim is meritless, however, given the absence of any colorable reason to question his factual guilt. The corroboration requirement serves the function of assuring that confessions represent a truthful representation of the facts, thereby confirming factual guilt.
See Emery v. State,
.
See, e.g., Motley v. State,
. For example, defense counsel implied that Carter might have committed other criminal acts, questioned whether he could — and should— live in society, wondered aloud whether death was a greater punishment than life imprisonment, and conceded that the jury could senteijce him death with a clear conscience.
.
See Kirkpatrick v. Butler,
. See Lackey v. Johnson,
