PATRICK E. HIGGINBOTHAM, Circuit Judge:

David Earl Gibbs has been on death row in Texas for the past twelve years following his conviction by a jury for raping and cutting the throat of Marietta Bryant in the course of a burglary of her apartment in Conroe, Texas, on the night of July 1, 1985. Gibbs also raped and killed Carol Ackland, Ms. Bryant’s roommate that evening in the apartment, but the state charged only the assault and death of Marietta Bryant.

Gibbs petitions the federal courts to set aside his conviction and sentences contending the State of Texas violated his constitutional rights in two ways: the prosecution failed to disclose evidence relevant to the jury’s sentencing decision, and the state trial judge admitted evidence of an offense for which he had been found innocent. Gibbs also urges that the federal district court denied Gibbs the opportunity to conduct discovery in support of his federal habeas petition. The United States District Court denied relief and refused a certificate of probable cause. After briefing and oral argument we also refuse the certificate.

The Texas Court of Criminal Appeals affirmed Gibbs’s conviction and sentence on direct appeal, Gibbs v. State, 819 S.W.2d 821 (Tex.Crim.App.1991), and the Supreme Court denied his petition for writ of certiorari on February 24, 1995. Judge Olen Underwood of the 284th District Court, Montgomery County, Texas, recommended denial of Gibbs’s Second Application for Writ of Habe-as Corpus on July 14, 1995, and Gibbs filed his federal petition three days later. The federal district court denied relief on May 15, 1997, and refused to issue a certificate of probable cause, but left its stay of execution in place. Gibbs filed his Application for Certificate of Probable Cause on November 24, 1997. Briefing was completed on April 20, 1998, and we heard argument on August 17, 1998.

The standard for granting a certificate of probable cause is whether Gibbs has made a substantial showing that he was denied a federal right. Barefoot v. Estelle, 463 U.S. 880, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983). The AEDPA is not applicable, and we moved to the merits of the appeal with briefs and oral argument rather than decide the request for a certificate of probable cause without that assistance. This insistence on a better look does not necessarily signal probable.cause. Some eases become clear with the benefit of full briefing and oral argument, leaving the ease one about which reasonable jurists would not differ. This is such a case.

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Gibbs’s main contention is that in the punishment phase of trial the prosecution called Roy Moody, who testified that Gibbs had assaulted him in their cell, but failed to disclose that prison officials had dismissed disciplinary charges against Gibbs arising from the incident. Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), imposes an affirmative duty to disclose to the defense evidence that is both favorable to the accused and material either to guilt or to punishment, including impeachment evidence. See United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985).

The principles governing the duty of the prosecutors to disclose evidence material to the defense, Brady material, are now easily stated if not always easily applied. Violation of the duty to disclose does not turn *256 on good or bad faith. Rather, it is the character of evidence, not the character of the prosecutor that matters. See United States v. Agurs, 427 U.S. 97, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976). A defendant must show that the withheld evidence could reasonably be taken to put the case in a different light so as to undermine confidence in the verdict. Kyles v. Whitley, 514 U.S. 419, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). At the same time, “[t]he mere possibility that an item of undisclosed information might have helped the defense, or might have affected the outcome of the trial, does not establish ‘materiality’ in the constitutional sense.” Agurs, 427 U.S. at 109-10, 96 S.Ct. 2392. There is no duty to furnish a defendant with exculpatory evidence that is fully available to the defendant though the exercise of reasonable diligence. Rector v. Johnson, 120 F.3d 551 (5th Cir.1997), cert. denied, — U.S. -, 118 S.Ct. 1061, 140 L.Ed.2d 122 (1998). Re-latedly, we have found no constitutional error in failing to disclose evidence contrary to the prosecutor’s assertions in closing argument, where the defendant would have known about the “withheld” evidence. West v. Johnson, 92 F.3d 1385, 1399 (5th Cir.1996), cert. denied, — U.S. -, 117 S.Ct. 1847, 137 L.Ed.2d 1050 (1997). At the same time, a prosecutor’s duty to disclose is not defined by his knowledge. It is no answer that the prosecutor did not know of exculpatory evidence, even in the hands of another arm of the state. See United States v. Auten, 632 F.2d 478, 481 (5th Cir.1980).

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Moody was not listed as a witness before trial. The prosecutor first disclosed to the defense and the. court that it intended to call Moody on the morning that he testified. The prosecutor explained that he had just learned of Moody and had brought him to trial from the state prison where he was an inmate. He informed the court that Moody was expected to testify about Gibbs’s assault of him in a jail cell. The trial judge overruled Gibbs’s objection that the witness had' not been previously disclosed and denied his request to continue the trial long enough to allow the defense to prepare for the witness. Moody testified as follows:

Q: Did you have occasion to have any land of confrontation or fight with Mr. Gibbs back on January 15th?

A: Yes; we did.

Q: Would you tell the jury in your own words what happened, please?

A: I asked him to turn his radio down ’cause it woke me up and he said no, so I unplugged it and that’s when he hit me in this eye and then hit me over here in the ear and then pounded with both hands on the back of my neck and choked me and told me he’d kill me.

Q: And, this happened on January 15th?

A: I’m not sure.

Q: Around that time anyway?

A: Yeah.

Q: Had you done anything other than unplug the radio?

A: No; I did not.

Q: Had you and he ever had any problems before?

A: No.

Q: Did you ever see the defendant get in a fight or beat up on anybody else while you were up there in that cell?

A: One other person.

Q: Would you tell the jury what you saw?

A: David jumped across the table and beat the hell out of that boy.

Defense counsel’s cross examination suggested provocation. There was no hint that Gibbs acted in self defense. The prosecutor in his closing argument referred to Moody’s testimony, pointing out Gibbs’s violent tendencies even in the controlled circumstance of confinement. It is plain that the prosecutor thought the testimony helpful to the state’s case — given his scramble to produce the witness in the middle of the sentencing phase and his use of the testimony in his close.

' Nearly a decade later in the course of developing a habeas petition, defense counsel found in the prosecutor’s files a jail record (Montgomery County Jail incident report) regarding the incident bearing the notation “:Dism:Self Defense.” Montgomery County *257 Sheriffs Department Officer Jack McKeon, commander of the jail in 1986 during the time of the incident, made the notation but later suffered a series of strokes and is unable' to testify.

The incident occurred on January 15,1986, at 5:20. According to jail records, Gibbs signed an offense report advising, “You are charged with violation of the Montgomery County Jail Rules 003-Fighting w/another person.” The notice read:

You will appear before the disciplinary committee of the Montgomery County Jail within Seven (7) but not less than twenty four (24) hours, to answer to the charges brought against you.

If found guilty, you have the right to appeal the decision of the committee in writing to the jail captain. The jail captain's decision will be final and returned to you within ten (ten) days. This appeal must be initiated within ten (10) days from the date of their decision. •

Moody appeared at the punishment phase of the trial on March 19, 1986, long after the disciplinary hearing set for January 22,1986.

The jail offense report had additional information about the incident:

On 01.15.86 at approximately 5:20 p.m. I, Sgt. Jones and Deputy P. Harris • were working the 4th floor desk when I Sgt. Jones heard our medic R. Owens hollar [sic] for me, Sgt. Jones that there was a fight in L-2. Deputy Harris being in front of the booking desk was the first to respond. Upon opening the door to L-2, Deputy P. Harris found-inmate Roy Moody on his hands and knees bent over with his hands on his head.

After getting coverage at the 4th floor desk I, Sgt. Jones went upstairs and entered L-2. I found inmate Roy Moody standing in the corner of the day room. All of L-2 started saying that R. Moody was having a bad dream.

After looking at R. Moody I noticed he had some redness around the left eye. I pulled R. Moody out of L-2 and asked him what happened. He said that David Earl Gibbs had hit him and tried to choke him_I Sgt. Jones seen [sic] what appeared to be red marks around R. Moody’s throat and found redness around his left eye. I asked R. Moody if he wanted to press charges.

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The state called six witnesses in the punishment phase, including Moody. The witnesses testified that Gibbs bragged about fights he had been in; spent most of his teenage years and adult life in foster homes, jails, and prisons; had observed his mother having sexual relations with another woman; and had attempted suicide. There was testimony that Gibbs was not violent when sober and-liked prison life. Charlie Thomas testified that several weeks after he fired Gibbs for stealing some checks , from his business Gibbs broke into Thomas’s apartment, found Thomas’s rifle, and threatened to kill Thomas, although Thomas talked him out of it, later buying him a beer. The defense called four mitigation witnesses, including co-workers at a convalescent center who testified that Gibbs was a good worker and well-mannered. A social worker testified that Gibbs confided in her that his mother had taught him to rob and steal as a young boy;, that he got along well in a half-way house such that she let him stay with her family on occasion.

- This summary of the range of evidence before the jury in the punishment phase of trial affords context for judging the failure to disclose the record with the notation of dismissal. We begin and end with the question of materiality. Gibbs fashions his argument upon a base that will not support it. The contention is that the notation on the record was information withheld from Gibbs. Whether or not Gibbs knew of the notation on the record, and there is no evidence that he did, he certainly knew if he had been disciplined for the incident. His counsel’s cross examination never touched self defense and never asked if 'Gibbs had been disciplined by jail authorities, a fact, if true, also known by Gibbs.

Significantly, the state did not rely upon a judgment of conviction or other paper record to prove prior misconduct. Rather, the state relied upon the testimony of the victim of *258 fered at trial and subject to cross examination by the defendant. The contention is that Gibbs could have used the notation on the records to challenge Moody’s version of the fight. But without Gibbs’s supporting testimony or some explanation of what the notation meant its value was equivocal at best. The notation is undated and unsigned. The state trial judge found in collateral proceedings that the prosecutors who tried the case were unaware of the notation. It was not until June, 1995, nearly ten years later, that it was found, apparently by Gibbs’s ha-beas counsel.

Gibbs never asserted at trial that he acted in self defense. Indeed, he has yet to do so. Gibbs knew as well as anyone if he acted in self defense and knew, as we have observed, that no disciplinary action was even taken against him, if that was the ease. And he knew that disciplinary procedures had been initiated because he signed the notice of charges. Given its equivocal meaning, the notation in hand at trial unsupported by other evidence would be of little assistance, and that is the only arguably exculpatory evidence not disclosed to him. If he had not 'acted in self defense and the notation was inaccurate, offering it into" evidence also would have put the disciplinary proceedings in play, entailing the risk of correcting proof. Finally, the balance of the report detailed the contemporaneous complaint of Moody. It supports his trial testimony. This prior consistent statement would have been admissible on the offer of the state to rebut an implication of recent fabrication. The contemporaneous complaint might have been admitted on some other ground. It surely would have, had the defense attempted to make use of the notation of dismissal. The point is that in judging the materiality of the notation we cannot ignore the cross-cutting price of its use by the defense.

Ill

Gibbs’s second claim also points to the incident involving Moody, contending that the state relied upon inaccurate evidence of a prior offense in violation of the Eight Amendment, a principle announced in Johnson v. Mississippi, 486 U.S. 578, 108 S.Ct. 1981, 100 L.Ed.2d 575 (1988). In Johnson the Supreme Court vacated Johnson’s conviction because the state had relied upon a prior conviction of first-degree rape reversed after Johnson’s capital trial.

We are not persuaded. In Johnson the invalidated conviction was the sole evidence of the prior conduct. The court in Johnson emphasized that because the- prosecutor relied upon a judgment of conviction to prove the prior acts, the reversal took away the prosecutor’s evidence. The evidence of Gibbs’s prior acts was the testimony at trial of the victim.

Gibbs contends that state and federal courts refused to allow discovery in support of his habeas petitions contrary to principles announced in Bracy v. Gramley, 520 U.S. 899, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997). Bracy did not lower the gate to discovery in habeas cases. Rather, the Court applied the standards of Harris v. Nelson, 394 U.S. 286, 89 S.Ct. 1082, 22 L.Ed.2d 281 (1969), that “where specific allegations before the court show reason to believe that the petitioner may, if the facts are fully developed, be able to demonstrate that he is .:. entitled to relief, it is the duty of the courts to provide the necessary facilities and procedures for an adequate inquiry.” Harris, 394 U.S. at 299, 89 S.Ct. 1082, quoted in Bracy, 520 U.S. at -, 117 S.Ct. at 1799. Rule 6[a], Rules Governing Sec. 2254 Cases requires a demonstration of “good cause.” Harris led to the adoption of Rule 6, and the rule was meant to be consistent with it, as Chief Justice Rehnquist pointed out in Bracy. Id. at -, 117 S.Ct. at 1799. He also accented that Bracy had made “specific allegations” and that the “scope and extent of such discovery is a matter confided to the discretion of the District Court.” Id.

Gibbs hoped discovery would develop evidence supporting claims that the state withheld evidence regarding the background of Texas Ranger Wesley Styles and that his lawyer was ineffective in not investigating Styles’ background. Ranger Styles questioned Gibbs on several occasions and testified at a suppression hearing regarding *259 Gibbs’s confession. Gibbs testified at the suppression hearing about threats, intimidation, physical abuse, and psychological coercion Styles is said to have used, including a promise that he would not pursue capital murder charges if Gibbs confessed.

First, with regard to the claim that discovery was needed to develop a possible claim that the government withheld exculpatory information regarding Ranger Styles, we are pointed to no non-public information or type of information directly relevant to the testimony of Styles. His asserted misconduct in other investigations was widely reported in the press. Regardless, Gibbs failed to explain the materiality to his case of any such information.

The state habeas court held that specific instances of Styles’ alleged misconduct were inadmissible under Texas law. As a federal court in a habeas review of a state court conviction, we cannot review state rulings on state law that do not present a federal constitutional question. And the nuances of state rules for impeaching a witness by prior acts of misconduct do not do so.

Gibbs had the full opportunity to cross examine Styles at the suppression hearing. As for a possible claim that Gibbs’s counsel was ineffective, his defense counsel asserted in affidavits that they knew of allegations concerning Styles in the Brandley case [a widely reported case of a prisoner ultimately released from the Texas prison system], but any misconduct would not have been admissible.

Gibbs’s claim ultimately rests on an expansive reading of Bracy that we cannot embrace. He argues that it is no answer that the discovery venture rests on speculation, because the purpose of discovery is just that — to discover. The argument continues that while reports about Ranger Styles were public, the defense needed to nail down witnesses and documents for trial. To what end, however, Gibbs does not fully answer. The best offered explanation is a possible development of opinion testimony regarding reputation for truthfulness or evidence that Styles was guilty of misconduct in other cases. ■ That speculation about evidence found by the state court to be likely inadmissible is not enough — at least not for us to find an abuse of discretion. In sum, we agree with the district court that Gibbs did not make the kind of particularized allegations or showing demanded by Bracy. This judgment call by the district court falls well within its discretion, given the deference it is due.

We vacate the stay of execution. The application for a certificate of probable cause is denied.