opinion: Justice Ginsburg
  delivered the opinion of the Court.
  Petitioner Delma Banks, Jr., was convicted of capital murder and sentenced to death. Prior to trial, the State advised Banks’s attorney there would be no need to litigate discovery issues, representing: “[W]e will, without the necessity of motions[,] provide you with all discovery to which you are entitled.” App. 361, n. 1; App. to Pet. for Cert. A4 (both sources’ internal quotation marks omitted). Despite that undertaking, the State withheld evidence that would have allowed Banks to discredit two essential prosecution witnesses. The State did not disclose that one of those witnesses was a paid police informant, nor did it disclose a pretrial transcript revealing that the other witness’ trial testimony had been intensively coached by prosecutors and law enforcement officers.
  Furthermore, the prosecution raised no red flag when the informant testified, untruthfully, that he never gave the police any statement and, indeed, had not talked to any police officer about the case until a few days before the trial. Instead of correcting the informant’s false statements, the prosecutor told the jury that the witness “ha[d] been open and honest with you in every way,” App. 140, and that his testimony was of the “utmost significance,” id., at 146. Similarly, the prosecution allowed the other key witness to convey, untruthfully, that his testimony' was entirely unrehearsed. Through direct appeal and state collateral review proceedings, the State continued to hold secret the key witnesses’ links to the police and allowed their false statements to stand uncorrected.
  Ultimately, through discovery and an evidentiary hearing authorized in a federal habeas corpus proceeding, the long-suppressed evidence came to light. The District Court granted Banks relief from the death penalty, but the Court of Appeals reversed. In the latter court’s judgment, Banks had documented his claims of prosecutorial misconduct too late and in the wrong forum; therefore he did not qualify for federal-court relief. We reverse that judgment. When police or prosecutors conceal significant exculpatory or impeaching material in the State’s possession, it is ordinarily incumbent on the State to set the record straight.
  I
  On April 14, 1980, police found the corpse of 16-year-old Richard Whitehead in Pocket Park, east of Nash, Texas, a town in the vicinity of Texarkana. Id., at 8,141. A preliminary autopsy revealed that Whitehead had been shot three times. Id., at 10. Bowie County Deputy Sheriff Willie Huff, lead investigator of the death, learned from two witnesses that Whitehead had been in the company of petitioner, 21-year-old Delma Banks, Jr., late on the evening of April 11. Id., at 11-15,144; Banks v. State, 643 S. W. 2d 129, 131 (Tex. Crim. App. 1982) (en banc), cert. denied, 464 U. S. 904 (1983). On April 23, Huff received a call from a con-fidentiál informant reporting that “Banks was coming to Dallas to meet an individual and get a weapon.” App. 15. That evening, Huff and other officers followed Banks to South Dallas, where Banks visited a residence. Ibid.; Brief for Petitioner 3. Police stopped Banks’s vehicle en route from Dallas, found a handgun in the car, and arrested the car’s occupants. App. 16. Returning to the Dallas residence Banks had visited, Huff encountered and interviewed Charles Cook and recovered a second gun, a weapon Cook said Banks had left with him several days earlier. Ibid. Tests later identified the second gun as the Whitehead murder weapon. Id., at 17.
  In a May 21,1980, pretrial hearing, Banks’s counsel sought information from Huff concerning the confidential informant who told Huff that Banks would be driving to Dallas. Id., at 21. Huff was unresponsive. Ibid. Any information that might reveal the identity of the informant, the prosecution urged, was privileged. Id., at 23. The trial court sustained the State’s objection. Id., at 24. Several weeks later, in a July 7, 1980, letter, the prosecution advised Banks’s counsel that “[the State] will, without necessity of motions provide you with all discovery to which you are entitled.” Id., at 361, n. 1; App. to Pet. for Cert. A4 (both sources’ internal quotation marks omitted).
  The guilt phase of Banks’s trial spanned two days in September 1980. See Brief for Petitioner 2; App. to Pet. for Cert. C3. Witnesses testified to seeing Banks and Whitehead together on April 11 in Whitehead’s green Mustang, and to hearing gunshots in Pocket Park at 4 a.m. on April 12. Banks v. State, 643 S. W. 2d, at 131. Charles Cook testified that Banks arrived in Dallas in a green Mustang at about 8:15 a.m. on April 12, and stayed with Cook until April 14. App. 42-43,47-53. Cook gave the following account of Banks’s visit. On the morning of his arrival, Banks had blood on his leg and told Cook “he [had] got into it on the highway with a white boy.” Id., at 44. That night, Banks confessed to having “kill[ed] the white boy for the hell of it and take[n] his car and come to Dallas.” . Id., at 48. During their ensuing conversation, Cook first noticed that “[Banks] had a pistol.” Id., at 49. Two days later, Banks left Dallas by bus. Id., at 52-53. The next day, Cook abandoned the Mustang in West Dallas and sold Banks’s gun to a neighbor. Id., at 54. Cook further testified that, shortly before the police arrived at his residence to question him, Banks had revisited him and requested the gun. Id., at 57.
  On cross-examination, Cook three times represented that he had not talked to anyone about his testimony. Id., at 59. In fact, however, Cook had at least one “pretrial practice sessio[n]” at which Huff and prosecutors intensively coached Cook for his appearance on the stand at Banks’s trial. Id., at 325, ¶ 10, 381-390; Joint Lodging Material 1-36 (transcript of pretrial preparatory session). The prosecution allowed Cook’s misstatements to stand uncorrected. In its guilt-phase summation, the prosecution told the jury “Cook brought you absolute truth.” App. 84.
  In addition to Cook, Robert Farr was a key witness for the prosecution. Corroborating parts of Cook’s account, Farr testified to traveling to Dallas with Banks to retrieve Banks’s gun. Id., at 34-35. On cross-examination, defense counsel asked Farr whether he had “ever taken any money from some police officers,” or “give[n] any police officers a statement.” Id., at 37-38. Farr answered no to both questions; he asserted emphatically that police officers had not promised him anything and that he had “talked to no one about this [case]” until a few days before trial. Ibid. These answers were untrue, but the State did not correct them. Farr was the paid informant who told Deputy Sheriff Huff that Banks would travel to Dallas in search óf a gun. Id., at 329; App. to Pet. for Cert. A4, A9. In a 1999 affidavit, Farr explained:
  “I assumed that if I did not help [Huff] with his investigation of Delma that he would have me arrested for drug charges. That’s why I agreed to help [Huff]. I was afraid that if I didn’t help him, I would be arrested. . . . “Willie Huff asked me to help him find Delma’s gun. I told [Huff] that he would have to pay me money right away for my help on the case. I think altogether he gave me about $200.00 for helping him. He paid me some of the money before I set Delma up. He paid me the rest after Delma was arrested and charged with murder....
  “In order to help Willie Huff, I had to set Delma up. I told Delma that I wanted to rob a pharmacy to get drugs and that I needed his gun to do it. I did not really plan to commit a robbery but I told Delma this so that he would give me his gun. ... I convinced Delma to drive to Dallas with me to get the gun.” App. 442-443, ¶ ¶ 6-8.
  The defense presented no evidence. App. to Pet. for Cert. A6. Banks was convicted of murder committed in the course of a robbery, in violation of Tex. Penal Code Ann. § 19.03(a)(2) (1974). See App. to Pet. for Cert. C3.
  The penalty phase ran its course the next day. Ibid. Governed by the Texas statutory capital murder scheme applicable in 1980, the jury decided Banks’s sentence by answering three “special issues.” App. 142-143. “If the jury unanimously answer[ed] ‘yes’ to each issue submitted, the trial court [would be obliged to] sentence the defendant to death.” Penry v. Lynaugh, 492 U. S. 302, 310 (1989) (construing Texas’ sentencing scheme); Tex. Code Crim. Proc. Ann., Arts. 37.071(c)-(e) (Vernon Supp. 1980). The critical question at the penalty phase in Banks’s case was: “Do you find from the evidence beyond a reasonable doubt that there is a probability that the defendant, Delma Banks, Jr., would commit criminal acts of violence that would constitute a continuing threat to society?” App. 143 (internal quotation marks omitted).
  On this question, the State offered two witnesses, Vetrano Jefferson and Robert Farr. Id., at 104-113. Jefferson testified that, in early April 1980, Banks had struck him across the face with a gun and threatened to kill him. Id., at 104-106. Farr’s testimony focused once more on the trip to Dallas to fetch Banks’s gun. The gun was needed, Farr asserted, because “[w]e [Farr and Banks] were going to pull some robberies.” Id., at 108. According to Farr, Banks “said he would take care of it” if “there was any trouble during these burglaries.” Id., at 109. When the prosecution asked: “How did [Banks] say he would take care of it?” Farr responded: “[Banks] didn’t go into any specifics, but he said it would be taken care of.” Ibid.
  On cross-examination, defense counsel twice asked whether Farr had told Deputy Sheriff Huff of the Dallas trip. Ibid. The State remained silent as Farr twice perjuriously testified: “No, I did not.” Ibid. Banks’s counsel also inquired whether Farr had previously attempted to obtain prescription drugs by fraud, and, “up tight over that,” would “testify to anything anybody want[ed] to hear.” Id., at 110. Farr first responded: “Can you prove it?” Ibid. Instructed by the court to answer defense counsel’s questions, Farr again said: “No, I did not. . . .” Ibid.
  Two defense witnesses impeached Farr, but were, in turn, impeached themselves. James Kelley testified to Farr’s attempts to obtain drugs by fraud; the prosecution impeached Kelley by eliciting his close relationship to Banks’s girlfriend. Id., at 124-129. Later,. Kelley admitted to being drunk while on the stand. App. to Pet. for Cert. A13. Former Arkansas police officer Gary Owen testified that Farr, as a police informant in Arkansas, had given false information; the prosecution impeached Owen by bringing out his pending application for employment by defense counsel’s private investigator. App. 129-131.
  Banks’s parents and acquaintances testified that Banks was a “respectful, churchgoing young man.” App. to Pet. for Cert. A7; App. 137-139. Thereafter, Banks took the stand. He affirmed that he had “never before been convicted of a felony.” Id., at 134. Banks admitted striking Vetrano Jefferson in April 1980, and traveling to Dallas to obtain a gun in late April 1980. Id., at 134-136. He denied, however, any intent to participate in robberies, asserting that Farr alone had planned to commit them. Id., at 136-137. The prosecution suggested on cross-examination that Banks had been willing “to supply [Farr] the means and possible death weapon in an armed robbery case.” Id., at 137. Banks conceded as much. Ibid.
  During summation, the prosecution intimated that Banks had not been wholly truthful in this regard, suggesting that “a man doesn’t travel two hundred miles, or whatever the distance is from here [Texarkana] to Dallas, Texas, to supply a person with a weapon.” Id., at 143. The State homed in on Farr’s testimony that Banks said he would “take care” of any trouble arising during the robbery:
  “[Farr] said, ‘Man, you know, what i[f] there’s trouble?’ And [Banks] says, ‘Don’t worry about it. I’ll take care of it.’ I*think that speaks for itself, and I think you know what that means. ... I submit to you beyond a reasonable doubt that the State has again met its burden of proof, and that the answer to question number two [propensity to commit violent criminal acts] should also be yes.” Id., at 140,144. See also id., at 146-147.
  Urging Farr’s credibility, the prosecution called the jury’s attention to Farr’s admission, at. trial, that he used narcotics. Id., at 36, 140. Just as Farr had been truthful about his drug use, the prosecution suggested, he was also “open and honest with [the jury] in every way” in his penalty-phase testimony. Id., at 140. Farr’s testimony, the prosecution emphasized, was “of the utmost significance” because it showed “[Banks] is a danger to friends and strangers, alike.” Id., at 146. Banks’s effort to impeach Farr was ineffective, the prosecution further urged, because defense witness “Kelley kn[ew] nothing about the murder,” and defense witness Owen “wish[ed] to please his future employers.” Id., at 148.
  The jury answered yes to the three special issues, and the judge sentenced Banks to death. The Texas Court of Criminal Appeals denied Banks’s direct appeal. 643 S. W. 2d, at 135. Banks’s first two state postconviction motions raised issues not implicated here; both were denied. Ex parte Banks, No. 13568-01 (Tex. Crim. App. 1984); Ex parte Banks, 769 S. W. 2d 539, 540 (Tex. Crim. App. 1989).
  Banks’s third state postconviction motion, filed January 13, 1992, presented questions later advanced in federal court and reiterated in the petition now before us. App. 150. Banks alleged “upon information and belief” that “the prosecution knowingly failed to turn over exculpatory evidence as required by [Brady v. Maryland, 373 U. S. 83 “(1963)]”; the withheld evidence, Banks asserted, “would have revealed Robert Farr as a police informant and Mr. Banks’ arrest as a set-up.” App. 180, ¶ 114 (internal quotation marks omitted). In support of this third state-court postconviction plea, Banks attached an unsigned affidavit from his girlfriend, Farr’s sister-in-law Demetra Jefferson, which stated that Farr “was well-connected to law enforcement people,” and consequently managed to stay out of “trouble” for illegally obtaining prescription drugs. Id., at 195, ¶7. Banks alleged as well that during the guilt phase of his trial, the State deliberately withheld information “critical to the jury’s assessment of Cook’s credibility,” including the “generous ‘deal’ [Cook had] cut with the prosecutors.” Id., at 152, ¶ 2, 180, ¶ 114.
  The State’s reply to Banks’s pleading, filed October 6,1992, “denie[d] each and every allegation of fact made by [Banks], except those supported by official court records and those specifically admitted.” Id., at 234; Tr. of Oral Arg, 32. “[N]othing was kept secret from the defense,” the State represented. App. 234. While the reply specifically asserted that the State had made “no deal with Cook,” ibid., the State said nothing specific about Farr. Affidavits from Deputy Sheriff Huff and prosecutors accompanied the reply. Id., at 241-243. The affiants denied any “deal, secret or otherwise, with Charles Cook,” but they, too, like the State’s pleading they supported, remained silent about Farr. Ibid.
  In February and July 1993 orders, the state postconviction court rejected Banks’s claims. App. to Pet. for Cert. E1-E9, G1-G7. The court found that “there was no agreement between the State and the witness Charles Cook,” but made no findings concerning Farr. Id., at G2. In a January 10, 1996, one-page per curiam order, the Texas Court of Criminal Appeals upheld the lower court’s disposition of Banks’s motion. Id., at Dl.
  On March 7, 1996, Banks filed the instant petition for a writ of habeas corpus in the United States District Court for the Eastern District of Texas. App. 248. He alleged multiple violations of his federal constitutional rights. App. to Pet. for Cert. C5-C7. Relevant here, Banks reasserted that the State had withheld material exculpatory evidence “reveal[ing] Robert Farr as a police informant and Mr. Banks’ arrest as a set-up.” App. 260, ¶ 152 (internal quotation marks omitted). Banks also asserted that the State had. concealed “Cook’s enormous incentive to testify in a manner favorable to the [prosecution].” Id., at 260, ¶ 153; App. to Pet. for Cert. C6-C7. In June 1998, Banks moved for discovery and an evidentiary hearing to gain information from the State on the roles played and trial testimony provided by Farr and Cook. App. 262-266, 282-283, 286. The superintending Magistrate Judge allowed limited discovery regarding Cook, but found insufficient justification for inquiries concerning Farr. Id., at 294-295.
  Banks renewed his discovery and evidentiary requests in February 1999. Id., at 2, 300-331. This time, he proffered affidavits from both Farr and Cook to back up his claims that, as to each of these two key witnesses, the prosecution had wrongly withheld crucial exculpatory and impeaching evidence. Id., at 322-331. Farr’s affidavit affirmed that Farr had “set Delma up” by proposing the drive to Dallas and informing Deputy Sheriff Huff of the trip. Id., at 329, ¶ 8, 442-443, ¶ 8; supra, at 678. Accounting for his unavailability earlier, Farr stated that less than a year after the Banks trial, he had left Texarkana, first for Oklahoma, then for California, because his police-informant work endangered his life. App. 330-331, 444; Pet. for Cert. 27, n. 12. Cook recalled that in preparation for his Banks trial testimony, he had participated in “three or four . . . practice sessions” at which prosecutors told him to testify “as they wanted [him] to, and that [he] would spend the rest of [his] life in prison if [he] did not.” App. 325, ¶¶ 10-11.
  On March 4, 1999, the Magistrate Judge an establishing issues for an evidentiary hearing, id., at 340, 346, at which she would consider Banks’s claims that the State had withheld “crucial exculpatory and impeaching evidence” concerning “two of the [S]tate’s essential witnesses, Charles Cook and Robert Farr,” id., at 340, 345 (internal quotation marks omitted). In anticipation of the hearing, the Magistrate Judge ordered disclosure of the Bowie County District Attorney’s files. Brief for Petitioner 37-38; Tr. of June 7-8, 1999, Federal Evidentiary Hearing (ED Tex.), p. 30 (hereinafter Federal Evidentiary Hearing).
  One item lodged in the District Attorney’s files, turned over to Banks pursuant to the Magistrate Judge’s disclosure order, was a 74-page transcript of a Cook interrogation. App. to Pet. for Cert. A10. The interrogation, conducted by Bowie County law enforcement officials and prosecutors, occurred in September 1980, shortly before the Banks trial. Ibid. The transcript revealed that the State’s representatives had closely rehearsed Cook’s testimony. In particular, the officials told Cook how to reconcile his testimony with affidavits to which he had earlier subscribed recounting Banks’s visits to Dallas. See, e. g., Joint Lodging Material 24 (“Your [April 1980] statement is obviously screwed up.”); id., at 26 (“[T]he way this statement should read is that....”); id., at 32 (“[Ljet me tell you how this is going to work.”); id., at 36 (“That’s not in your [earlier] statement.”). Although the transcript did not bear on Banks’s claim that the prosecution had a deal with Cook, it provided compelling evidence that Cook’s testimony had been tutored by Banks’s prosecutors. Without objection at the hearing, the Magistrate Judge admitted the September 1980 transcript into evidence. Brief for Petitioner 39; Federal Evidentiary Hearing 75-76.
  Testifying at the evidentiary hearing, Deputy Sheriff Huff acknowledged, for the first time, that Farr was an informant and that he had been paid $200 for his involvement in the case. App. to Pet. for Cert. C43. As to Cook, a Banks trial prosecutor testified, in line with the State’s consistent position, that no deal had been offered to gain Cook’s trial testimony. Id., at C45; Federal Evidentiary Hearing 52-53. Defense counsel questioned the prosecutor about the September 1980 transcript, calling attention to discrepancies between the transcript and Cook’s statements at trial. Id., at 65-68. In a posthearing brief and again in proposed findings of fact and conclusions of law, Banks emphasized the suppression of the September 1980 transcript, noting the prosecution’s obligation to disclose material, exculpatory evi-. dence, and the assurance in this case that Banks would receive “all [the] discovery to which [Banks was] entitled.” App. 360-361, and n. 1, 378-379 (internal quotation marks omitted); supra, at 677.
  In a May 11,2000, report and recommendation, the Magistrate Judge recommended a writ of habeas corpus with respect to Banks’s death sentence, but not his conviction. App. to Pet. for Cert. C54. “[T]he State’s failure to disclose Farr’s informant status, coupled with trial counsel’s dismal performance during the punishment phase,” the Magistrate Judge concluded, “undermined the reliability of the jury’s verdict regarding punishment.” Id., at C44. Finding no convincing evidence of a deal between the State and Cook, however, she recommended that the guilt-phase verdict remain undisturbed. Id., at C46.
  Banks moved to alter or amend the Magistrate Judge’s report on the ground that it left unresolved a fully aired question, i e., whether Banks’s rights were violated by the State’s failure to disclose to the defense the prosecution’s eve-of-trial interrogation of Cook. App. 398. That interrogation, Banks observed, could not be reconciled with Cook’s insistence at trial that he had talked to no one about his testimony. Id., at 400, n. 17; see supra, at 677.
  The District Court adopted the Magistrate Judge’s report and denied Banks’s motion to amend the report. App. to Pet. for Cert. B6; App. 421-424. Concerning the Cook Brady transcript-suppression claim, the District Court recognized that Banks had filed his federal petition in 1996, three years before he became aware of the September 1980 transcript. App. 422-423. When the transcript surfaced in response to the Magistrate Judge’s 1999 disclosure order, Banks raised that newly discovered, long withheld document in his proposed findings of fact and conclusions of law and, again, in his objections to the Magistrate Judge’s report. Id., at 423. The District Court concluded, however, that Banks had not properly pleaded a Brady claim predicated on the withheld Cook rehearsal transcript. App. 422. When that Brady claim came to light, the District Court reasoned, Banks should have moved to amend or supplement his 1996 federal habeas petition specifically to include the 1999 discovery as a basis for relief. App. 423. Banks urged that a Brady claim based on the September 1980 transcript had been aired by implied consent; under Federal Rule of Civil Procedure 15(b), he contended, the claim should have been treated as if raised in the pleadings. App. 433. Banks sought, and the District Court denied, a certificate of appeal-ability on this question. Id., at 433, 436.
  In an August 20, 2003, unpublished per curiam opinion, the Court of Appeals for the Fifth Circuit reversed the judgment of the District Court to the extent that it granted relief on the Farr Brady claim and denied a certificate of appeal-ability on the Cook Brady claim. App. to Pet. for Cert. A2, judgt. order reported at 48 Fed. Appx. 104 (2002). The Court of Appeals observed that in his 1992 state-court post-conviction application, Banks had not endeavored to develop the facts underpinning the Farr Brady claim. App. to Pet. for Cert. A19-A20. For that reason, the court held, the evi-dentiary proceeding ordered by the Magistrate Judge was unwarranted. Ibid. The Court of Appeals expressed no doubt that the prosecution had suppressed, prior to the federal habeas proceeding, Farr’s informant status and his part in the fateful trip to Dallas. But Banks was not appropriately diligent in pursuing his state-court application, the Court of Appeals maintained. In the Fifth Circuit’s view, Banks should have at that time attempted to locate Farr and question him; similarly, he should have asked to interview Deputy Sheriff Huff and other officers involved in investigating the crime. Id., at A19, A22. If such efforts had proved unavailing, the Court of Appeals suggested, Banks might have applied to the state court for assistance. Id., at A19. Banks’s lack of diligence in pursuing his 1992 state-court plea, the Court of Appeals concluded, rendered the evidence uncovered in the federal habeas proceeding procedurally barred. Id., at A22-A23.
  In any event, the Fifth Circuit further concluded, Farr’s status as an informant was not “materia[l]” for Brady purposes. App. to Pet. for Cert. A32-A33. Banks had impeached Farr at trial by bringing out that he had been a police informant in Arkansas, and an unreliable one at that. Id., at A28, A32-A33; supra, at 680. Moreover, the Court of Appeals said, other witnesses had corroborated much of Farr’s testimony against Banks. App. to Pet. for Cert. A32. Notably, Banks himself had acknowledged his willingness to get a gun for Farr’s use in robberies. Ibid. In addition, the Fifth Circuit observed, the Magistrate Judge had relied on the cumulative effect of Brady error and the ineffectiveness of Banks’s counsel at the penalty phase. App. to Pet. for Cert. A44. Banks himself, however, had not urged that position; he had argued Brady and ineffective assistance of counsel discretely, not cumulatively. App. to Pet. for Cert. A46-A47. Finally, in accord with the District Court, the Court of Appeals apparently regarded Rule 15(b) as inapplicable in habeas proceedings. App. to Pet. for Cert. A51-A52. The Fifth Circuit accordingly denied a certificate of appealability on the Cook Brady transcript-suppression claim. App. to Pet. for Cert. A52, A78.
  With an execution date set for March 12, 2003, Banks applied to this Court for a writ of certiorari, presenting four issues: the tenability of his Farr Brady claim; a penalty-phase ineffective-assistance-of-counsel claim; the question whether, as to the Cook Brady transcript-suppression claim, a certificate of appealability was wrongly denied; and a claim of improper exclusion of minority jurors in violation of Swain v. Alabama, 380 U. S. 202 (1965). Pet. for Cert. 23-24. We stayed Banks’s execution on March 12, 2003, 538 U. S. 917, and, on April 21, 2003, granted his petition on all questions other than his Swain claim. 538 U. S. 977. We now reverse the Court of Appeals’ judgment dismissing Banks’s Farr Brady claim and that Court’s denial of a certificate of appealability on his Cook Brady claim.
  II
  We note, initially, that Banks s Brady claims arose under the regime in place prior to the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), 110 Stat. 1214. Turning to the tenability of those claims, we consider first Banks’s Farr Brady claim as it trains on his death sentence, see App. to Pet. for Cert. B6 (District Court granted habeas solely with respect to the capital sentence), and next, Banks’s Cook Brady claim.
  A
  To pursue habeas corpus relief in federal court, Banks first had to exhaust “the remedies available in the courts of the State;” 28 U. S. C. §2254(b) (1994 ed.); see Rose v. Lundy, 455 U. S. 509, 520 (1982). Banks alleged in his January 1992 state-court application for a writ of habeas corpus that the prosecution knowingly failed to turn over exculpatory evidence involving Farr in violation of Banks’s due process rights. App. 180. Banks thus satisfied the exhaustion requirement as to the legal ground for his Farr Brady claim.
  In state postconviction court, however, Banks failed to produce evidence establishing that Farr had served as a police informant in this case. As support for his Farr Brady claim, Banks appended to his state-court application only De-metra Jefferson’s hardly probative statement that Farr “was well-connected to law enforcement people.” App. 195, ¶ 7; see supra, at 682. In the federal habeas forum, therefore, it was incumbent on Banks to show that he was not barred, by reason of the anterior state proceedings, from producing evidence to substantiate his Farr Brady claim. Banks “[would be] entitled to an evidentiary hearing [in federal court] if he [could] show cause for his failure to develop the facts in state-court proceedings and actual prejudice resulting from that failure.” Keeney v. Tamayo-Reyes, 504 U. S. 1, 11 (1992).
  Brady, we reiterate, held that “the suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution.” 373 U. S., at 87. We set out in Strickler v. Greene, 527 U. S. 263, 281-282 (1999), the three components or essential elements of a Brady prosecutorial misconduct claim: “The evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently; and prejudice must have ensued.” 527 U. S., at 281-282. “[Clause and prejudice” in this case “parallel two of the three components of the alleged Brady violation itself.” Id., at 282. Corresponding to the second Brady component (evidence suppressed by the State), a petitioner shows “cause” when the reason for his failure to develop facts in state-court proceedings was the State’s suppression of the relevant evidence; coincident with the third Brady component (prejudice), prejudice within the compass of the “cause and prejudice” requirement exists when the suppressed evidence is “material” for Brady purposes. 527 U. S., at 282. As to the first Brady component (evidence favorable to the accused), beyond genuine debate, the suppressed evidence relevant here, Farr’s paid informant status, qualifies as evidence advantageous to Banks. See App. to Pet. for Cert. A26 (Court of Appeals’ recognition that “Farr’s being a paid informant would certainly be favorable to Banks in attacking Farr’s testimony”). Thus, if Banks succeeds in demonstrating “cause and prejudice,” he will at the same time succeed in establishing the elements of his Farr Brady death penalty due process claim.
  B
  Our determination as to “cause” for Banks’s failure to develop the facts in state-court proceedings is informed by Strickler: In that case, Virginia prosecutors told the petitioner, prior to trial, that “the prosecutor’s files were open to the petitioner’s counsel,” thus “there was no need for a formal [Brkdy] motion.” 527 U. S., at 276, n. 14 (quoting App. in Strickler v. Greene, O. T. 1998, No. 98-5864, pp. 212-213 (brackets in original)). The prosecution file given to the Strickler petitioner, however, did not include several documents prepared by an “importan[t]” prosecution witness, recounting the witness’ initial difficulty recalling the events to which she testified at the petitioner’s trial. 527 U. S., at 273-275, 290. Those absent-from-the-file documents could have been used to impeach the witness. Id., at 273. In state-court postconviction proceedings, the Strickler petitioner had unsuccessfully urged ineffective assistance of trial counsel based on counsel’s failure to move, pretrial, for Brady material. Answering that plea, the State asserted that a Brady motion would have been superfluous, for the prosecution had maintained an open file policy pursuant to which it had disclosed all Brady material. 527 U. S., at 276, n. 14, 278.
  This Court determined that in the federal habeas proceedings, the Strickler petitioner had shown cause for his failure to raise a Brady claim in state court. 527 U. S., at 289. Three factors accounted for that determination:
  “(a) the prosecution withheld exculpatory evidence; (b) petitioner reasonably relied on the prosecution’s open file policy as fulfilling the prosecution’s duty to disclose such evidence; and (c) the [State] confirmed petitioner’s reliance on the open file policy by asserting during state habeas proceedings that petitioner had already received everything known to the government.” Ibid, (internal quotation marks omitted).
  This case is congruent with Strickler in all three respects. First, the State knew of, but kept back, Farr’s arrangement with Deputy Sheriff Huff. App. to Pet. for Cert. C43; Tr. of Oral Arg. 33; cf. Kyles v. Whitley, 514 U. S. 419, 437 (1995) (prosecutors are responsible for “any favorable evidence known to the others acting on the government’s behalf in the case, including the police”). Second, the State asserted, on the eve of trial, that it would disclose all Brady material. App. 361, n. 1; see supra, at 677. As Strickler instructs, Banks cannot be faulted for relying on that representation. See 527 U. S., at 283-284 (an “open file policy” is one factor that “explain [s] why trial counsel did not advance [a Brady] claim”).
  Third, in his January 1992 state habeas application, Banks asserted that Farr was a police informant and Banks’s arrest, “a set-up.” App. 180, ¶ 114 (internal quotation marks omitted). In its answer, the State denied Banks’s assertion. Id., at 234; see supra, at 683. The State thereby “confirmed” Banks’s reliance on the prosecution’s representation that it had fully disclosed all relevant information its file contained. 527 U, S., at 289; see id., at 284 (state habeas counsel, as well as trial counsel, could reasonably rely on the State’s representations). In short, because the State persisted in hiding Farr’s informant status and misleadingly represented that it had complied in full with its Brady disclosure obligations, Banks had cause for failing to investigate, in state postconviction proceedings, Farr’s connections to Deputy Sheriff Huff.
  On the question of “cause,” moreover, Banks’s case is stronger than was the petitioner’s in Strickler in a notable respect. As a prosecution witness in the guilt and penalty phases of Banks’s trial, Farr repeatedly misrepresented his dealings with police; each time Farr responded untruthfully, the prosecution allowed his testimony to stand uncorrected. See supra, at 678-680. Farr denied taking money from or being promised anything by police officers, App. 37; he twice denied speaking with police officers, id., at 38, and twice denied informing Deputy Sheriff Huff about Banks’s trip to Dallas, id., at 109. It has long been established that the prosecution’s “deliberate deception of a court and jurors by the presentation of known false evidence is incompatible with rudimentary demands of justice.” Giglio v. United States, 405 U. S. 150, 153 (1972) (quoting Mooney v. Holohan, 294 U. S. 103, 112 (1935) (per curiam) (internal quotation marks omitted)). If it was reasonable for Banks to rely on the prosecution’s full disclosure representation, it was also appropriate for Banks to assume that his prosecutors would not stoop to improper litigation conduct to advance prospects for gaining a conviction. See Berger v. United States, 295 U. S. 78, 88 (1935); Strickler, 527 U. S., at 284.
  The State presents three main arguments for distinguishing Strickler on the issue of “cause,” two of them endorsed by the Court of Appeals. Brief for Respondent 15-20; App. to Pet. for Cert. A19, A22-A23; see supra, at 687-688. We conclude that none of these arguments accounts adequately for the State’s concealment and misrepresentation regarding Farr’s link to Deputy Sheriff Huff. The State first suggests that Banks’s failure, during state postconviction proceedings, to “attempt to locate Farr and ascertain his true status,” or to “interview the investigating officers, such as Deputy Huff, to ascertain Farr’s status,” undermines a finding of cause; the Fifth Circuit agreed. App. to Pet. for Cert. A22; Brief for Respondent 18-20. In the State’s view, “[t]he question [of cause] revolves around Banks’s conduct,” particularly his lack of appropriate diligence in pursuing the Farr Brady claim before resorting to federal court. Brief for Respondent 14.
  We rejected a similar argument in Strickler. There, the State contended that examination of a witness’ trial testimony, alongside a letter the witness published in a local newspaper, should have alerted the petitioner to the existence of undisclosed interviews of the witness by the police. 527 U. S., at 284, and n. 26. We found this contention insubstantial. In light of the State’s open file policy, we noted, “it is especially unlikely that counsel would have suspected that additional impeaching evidence was being withheld.” Id., at 285. Our decisions lend no support to the notion that defendants must scavenge for hints of undisclosed Brady material when the prosecution represents that all such material has been disclosed. As we observed in Strickler, defense counsel has no “procedural obligation to assert constitutional error on the basis of mere suspicion that some prosecutorial misstep may have occurred." 527 U. S., at 286-287. The “cause” inquiry, we have also observed, turns on events or circumstances “external to the defense.” Amadeo v. Zant, 486 U. S. 214, 222 (1988) -(quoting Murray v. Carrier, 477 U. S. 478, 488 (1986)).
  The State here nevertheless urges, in effect, that “the prosecution can lie and conceal and the prisoner still has the burden to .. . discover the evidence,” Tr. of Oral Arg. 35, so long as the “potential existence” of a prosecutorial misconduct claim might have been detected, id., at 36. A rule thus declaring “prosecutor may hide, defendant must seek,” is not tenable in a system constitutionally bound to accord defendants due process. “Ordinarily, we presume that public officials have properly discharged their official duties.” Bracy v. Gramley, 520 U. S. 899, 909 (1997) (quoting United States v. Chemical Foundation, Inc., 272 U. S. 1, 14-15 (1926) (internal quotation marks omitted)). We have several times underscored the “special role played by the American prosecutor in the search for truth in.criminal trials.” Strickler, 527 U. S., at 281; accord Kyles, 514 U. S., at 439-440; United States v. Bagley, 473 U. S. 667, 675, n. 6 (1985); Berger, 295 U. S., at 88. See also Olmstead v. United States, 277 U. S. 438, 484 (1928) (Brandeis, J., dissenting). Courts, litigants, and juries properly anticipate that “obligations [to refrain from improper methods to secure a conviction] . . . plainly resting] upon the prosecuting attorney, will be faithfully observed.” Berger, 295 U. S., at 88. Prosecutors’ dishonest conduct or unwarranted concealment should attract no judicial approbation. See Kyles, 514 U. S., at 440 (“The prudence of the careful prosecutor should not ... be discouraged.”).
  The State’s second argument is a variant of the first. Specifically, the State argues, and the Court of Appeals accepted, that Banks cannot show cause because in the 1992 state-court postconviction proceedings, he failed to move for investigative assistance enabling him to inquire into Farr’s police connections, connections he then alleged, but failed to prove. Brief for Respondent 15-16; App. to Pet. for Cert. A19; see 1977 Tex. Gen. Laws ch. 789, §2(d) (as amended) (instructing postconviction court to “designate] the issues of fact to be resolved,” and giving the court discretion to “order affidavits, depositions, interrogatories, and hearings”). Armed in 1992 only with Demetra Jefferson’s declaration that Farr was “well-connected to law enforcement people,” App. 195, ¶ 7; see supra, at 682, Banks had little to proffer in support of a request for assistance from the state post-conviction court. We assign no overriding significance to Banks’s failure to invoke state-court assistance to which he had no clear entitlement. Cf. Strickler, 527 U. S., at 286 (“Proper respect for state procedures counsels against a requirement that all possible claims be raised in state collateral proceedings, even when no known facts support them.”).
  Finally, relying on Roviaro v. United States, 353 U. S. 53 (1957), the State asserts that “disclosure [of an informant’s identity] is not automatic,” and, “[consequently, it was Banks’s duty to move for disclosure of otherwise privileged material.” Brief for Respondent 17-18, n. 15. We need not linger over this argument. The issue of evidentiary law in Roviaro was whether (or when) the Government is obliged to reveal the identity of an undercover informer the Government does not call as a trial witness. 353 U. S., at 55-56. The Court there stated that no privilege obtains “[w]here the disclosure of an informer’s identity, or of the contents of his communication, is relevant and helpful to the defense of an accused.” Id., at 60-61. Accordingly, even though the informer in Roviaro did not testify, we held that disclosure of his identity was necessary because he could have “amplified] or contradicted] the testimony of government witnesses.” Id., at 64.
  Here, the State elected to call Farr as a witness. Indeed, he was a key witness at both guilt and punishment phases of Banks’s capital trial. Farr’s status as a paid informant was unquestionably “relevant”; similarly beyond doubt, disclosure of Farr’s status would have been “helpful to [Banks’s] defense.” Id., at 60-61. Nothing in Roviaro, or any other decision of this Court, suggests that the State can examine an informant at trial, withholding acknowledgment of his informant status in the hope that defendant will not catch on, so will make no disclosure motion.
  In summary, Banks’s prosecutors represented at trial and in state postconviction proceedings that the State had held nothing back. Moreover, in state postconviction court, the State’s pleading denied that Farr was an informant. App. 234; supra, at 683. It was not incumbent on Banks to prove these representations false; rather, Banks was entitled to treat the prosecutor’s submissions as truthful. Accordingly, Banks has shown cause for failing to present evidence in state court capable of substantiating his Farr Brady claim.
  C
  Unless suppressed evidence is “material for Brady purposes, [its] suppression [does] not give rise to sufficient prejudice to overcome [a] procedural default.” Strickler, 527 U. S., at 282 (internal quotation marks omitted). Our touchstone on materiality is Kyles v. Whitley, 514 U. S. 419 (1995). Kyles instructed that the materiality standard for Brady claims is met when “the favorable evidence could reasonably be taken to put the whole case in such a different light as to undermine confidence in the verdict.” 514 U. S., at 435. See also id., at 434-435 (“A defendant need not demonstrate that after discounting the inculpatory evidence in light of the undisclosed evidence, there would not have been enough left to convict.”); accord Strickler, 527 U. S., at 290. In short, Banks must show a “reasonable probability of a different result.” Kyles, 514 U. S., at 434 (internal quotation marks omitted) (citing Bagley, 473 U. S., at 678).
  As the State acknowledged at oral argument, Farr was “paid for a critical role in the scenario that led to the indictment.” Tr. of Oral Arg. 34. Farr’s declaration, presented to the federal habeas court, asserts that Farr, not Banks, initiated the proposal to obtain a gun to facilitate the commission of robberies. See App. 442-443, ¶¶ 7 — 8; supra, at 678. Had Farr not instigated, upon Deputy Sheriff Huff’s request, the Dallas excursion to fetch Banks’s gun, the prosecution would have had slim, if any, evidence that Banks planned to “continue” committing violent acts. App. 147. Farr’s admission of his instigating role, moreover, would have dampened the prosecution’s zeal in urging the jury to bear in mind Banks’s “planning and acquisition of a gun to commit robbery,” or Banks’s “planned violence.” Ibid.; see Tr. of Oral Arg. 50.
  Because Banks had no criminal record, Farr’s testimony about Banks’s propensity to commit violent acts was crucial to the prosecution. Without that testimony, the State could not have underscored, as it did three times in the penalty phase, that Banks would use the gun fetched in Dallas to “take care” of trouble arising during the robberies. App. 140, 144, 146-147; see supra, at 681. The stress placed by the prosecution on this part of Farr’s testimony, uncorroborated by any other witness, belies the State’s suggestion that “Farr’s testimony was adequately corroborated.” Brief for Respondent 22-25. The prosecution’s penalty-phase summation, moreover, left no doubt about the importance the State attached to Farr’s testimony. What Farr told the jury, the prosecution urged, was “of the utmost significance” to show “[Banks] is a danger to friends and strangers, alike.” App. 146.
  In Strickler, 527 U. S., at 289, although the Court found “cause” for the petitioner’s procedural default of a Brady claim, it found the requisite “prejudice” absent, 527 U. S., at 292-296. Regarding' “prejudice,” the contrast between Strickler and Banks’s case is marked. The witness whose impeachment was at issue in Strickler gave testimony that was in the main cumulative, id., at 292, and hardly significant to one of the “two predicates for capital murder: [armed] robbery,” id., at 294. Other evidence in the record, the Court found, provided strong support for the conviction even if the witness’ testimony had been excluded entirely: Unlike the Banks prosecution, in Strickler, “considerable forensic and other physical evidence link[ed] [the defendant] to the crime” and supported the capital murder conviction. Id., at 293. Most tellingly, the witness’ testimony in Strickler “did not relate to [the petitioner’s] eligibility for the death sentence”; it “was not relied upon by the prosecution at all during its closing argument at the penalty phase.” Id., at 295. In contrast, Farr’s testimony was the centerpiece of Banks’s prosecution’s penalty-phase case.
  Farr’s trial testimony, critical at the penalty phase, was cast in large doubt by the declaration Banks ultimately obtained from Farr and introduced in the federal habeas proceeding. See supra, at 678, 684. In the guilt phase of •Banks’s trial, Farr had acknowledged his narcotics use. App. 36. In the penalty phase, Banks’s counsel asked Farr if, “drawn up tight over” previous drug-related activity, he would “testify to anything anybody want[ed] to hear”; Farr denied this. Id., at 110; supra, at 680. Farr’s declaration supporting Banks’s federal habeas petition, however, vividly contradicts that denial: “I assumed that if I did not help [Huff] ... he would have me arrested for drug charges.” App. 442, ¶ 6. Had jurors known of Farr’s continuing interest in obtaining Deputy Sheriff Huff’s favor, in addition to his receipt of funds to “set [Banks] up,” id., at 442, ¶ 7, they might well have distrusted Farr’s testimony, and, insofar as it was uncorroborated, disregarded it.
  The jury, moreover, did not benefit from customary, truth-promoting precautions that generally accompany the testimony of informants. This Court has long recognized the “serious questions of credibility” informers pose. On Lee v. United States, 343 U. S. 747, 757 (1952). See also Trott, Words of Warning for Prosecutors Using Criminals as Witnesses, 47 Hastings L. J. 1381, 1385 (1996) (“Jurors suspect [informants’] motives from the moment they hear about them in a case, and they frequently disregard their .testimony altogether as highly untrustworthy and unreliable . . . We have therefore allowed defendants “broad latitude to probe [informants’] credibility by cross-examination” and have counseled submission of the credibility issue to the jury “with careful instructions.” On Lee, 343 U. S., at 757; accord Hoffa v. United States, 385 U. S. 293, 311-312 (1966). See also 1A K. O’Malley, J. Grenig, & W. Lee, Federal Jury Practice and Instructions, Criminal §15.02 (5th ed. 2000) (jury instructions from the First, Fifth, Sixth, Seventh, Eighth, Ninth, and Eleventh Circuits on special caution appropriate in assessing informant testimony).
  The State argues that “Farr was heavily impeached [at trial],” rendering his informant status “merely cumulative.” Tr. of Oral Arg. 49; see Brief for Respondent 26-28; post, at 709, n. 3. The record suggests otherwise. Neither witness called to impeach Farr gave evidence directly relevant to Farr’s part in Banks’s trial. App. 124-133; id., at 129 (prosecutor noted that Kelley lacked “personal knowledge with regard to this case on trial”). The impeaching witnesses, Kelley and Owen, moreover, were themselves impeached, as the prosecution stressed on summation. See id., at 141,148; supra, at 680, 682. Further, the prosecution turned to its advantage remaining impeachment evidence concerning Farr’s drug use. On summation, the prosecution suggested that Farr's admission “that he used dope, that he shot,” demonstrated that Farr had been “open and honest with [the jury] in every way.” App. 140; supra, at 681.
  At least as to the penalty phase, in sum, one can hardly be confident that Banks received a. fair trial, given the jury’s ignorance of Farr’s true role in the investigation and trial of the case. See Kyles, 514 U. S., at 434 (“The question is not whether the defendant would more likely than not have received a different verdict with the evidence, but whether in its absence he received a fair trial, understood as a trial resulting in a verdict worthy of confidence.”). On the record before us, one could not plausibly deny the existence of the requisite “reasonable probability of a different result” had the suppressed information been disclosed to the defense. Ibid, (internal quotation marks omitted) (citing Bagley, 473 U. S., at 678); Strickler, 527 U. S., at 290. Accordingly, as to the suppression of Farr’s informant status and its bearing on “the reliability of the jury’s verdict regarding punishment,” App. to Pet. for Cert. C44; supra, at 686, all three elements of a Brady claim are satisfied.
  III
  Both the District Court and the Court of Appeals denied Banks a certificate of appealability with regard to his Cook Brady claim, which rested on the prosecution’s suppression of the September 1980 Cook interrogation transcript. App. 422-423; App. to Pet. for Cert. A52, A78; supra, at 687, 689. See also Joint Lodging Material 1-36. The District Court and the Fifth Circuit concluded that Banks had not properly pleaded this claim because he had not sought leave to amend his petition, but had stated the claim only in other submissions, i. e., in his proposed findings of fact and conclusions of law, and, again, in his objections to the Magistrate Judge’s report. App. 422-423, 432-433; App. to Pet. for Cert. A51-A52; supra, at 687, 689. Banks contended, unsuccessfully, that evidence substantiating the Cook Brady claim had been aired before the Magistrate Judge; therefore the claim should have been treated as if raised in the pleadings, as Federal Rule of Civil Procedure 15(b) instructs. See App. to Pet. for Cert. A51-A52; supra, at 687, n. 8 (setting out text of Rule 15(b)). The Fifth Circuit stated its position on this point somewhat obliquely, but appears to have viewed Rule 15(b) as inapplicable in habeas proceedings; the State now concedes, however, that the question whether Rule 15(b) extends to habeas proceedings is one “jurists of reason would find . . . debatable.” Compare App. to Pet. for Cert. A52 (quoting Slack v. McDaniel, 529 U. S. 473, 484 (2000)), with Tr. of Oral Arg. 45-46. We conclude that a certificate of appealability should have issued.
  We have twice before referenced Rule 15(b)’s application in federal habeas proceedings. In Harris v. Nelson, 394 U. S. 286, 294, n. 5 (1969), we noted that Rule 15(b)’s use in habeas proceedings is “noncontroversial.” In Withrow v. Williams, 507 U. S. 680, 696, and n. 7 (1993), we similarly assumed Rule 15(b)'s application to habeas petitions. There, however, the District Court had granted a writ of habeas corpus on a claim neither pleaded, considered at “an evidentiary hearing,” nor “even argu[ed]” by the parties. Id., at 695. Given those circumstances, we held that there had been no trial of the claim by implied consent; the respondent warden, we observed, “was manifestly prejudiced by the District Court's failure to afford her an opportunity to present evidence bearing on th[e] claim’s resolution.” Id., at 696. Here, in contrast, the issue of the undisclosed Cook interrogation transcript was indeed aired before the Magistrate Judge, and the transcript itself was admitted into evidence without objection. See supra, at 685.
  The Court of Appeals found no authority for equating “an evidentiary hearing ... with a trial” for Rule 15(b) purposes. App. to Pet. for Cert. A52. We see no reason why an evidentiary hearing should not qualify so long as the respondent gave “any sort of consent” and had a full and fair “opportunity to present evidence bearing on th[ej claim’s resolution.” Withrow, 507 U. S., at 696. Nor do we find convincing the Fifth Circuit’s view that applying Rule 15(b) in habeas proceedings would undermine the State’s exhaustion and procedural default defenses. Ibid. Under pre-AEDPA law, there was no inconsistency between Rule 15(b) and those defenses. That is doubtless why this Court’s pre-AEDPA cases assumed Rule 15(b)’s application in habeas proceedings. See ibid.; Harris, 394 U. S., at 294, n. 5. We note in this regard that, while AEDPA forbids a finding that exhaustion has been waived unless the State expressly waives the requirement, 28 U. S. C. § 2254(b)(3), under pre-AEDPA law, exhaustion and procedural default defenses could be waived based on the State’s litigation conduct. See Gray v. Netherland, 518 U. S. 152, 166 (1996) (failure to raise procedural default in federal habeas court means the defense is lost); Granberry v. Greer, 481 U. S. 129, 135 (1987) (“if a full trial has been held in the district court and it is evident that a miscarriage of justice has occurred, it may... be appropriate for the court of appeals to hold that the nonexhaustion defense has been waived”).
  To obtain a certificate of appealability, a prisoner must “demonstrate] that jurists of reason could disagree with the district court’s resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.” Miller-El. v. Cockrell, 537 U. S. 322, 327 (2003). At least as to the application of Rule 15(b), this case surely fits that description. A certificate of appealability, therefore, should have issued.
  * * *
  For the reasons stated, the judgment of the United States Court of Appeals for the Fifth Circuit is reversed, and the case is remanded for further proceedings consistent with this opinion.
  It is so ordered.
  Although a police officer testified Whitehead’s body was found on April 14, App. 8, the Texas Court of Criminal Appeals stated the body was discovered on April 15. Banks v. State, 643 S. W. 2d 129, 131 (1982) (en banc).
  “A person commits an offense if he commits murder . . . and . . . the person intentionally commits the murder in the course of committing or attempting to commit kidnapping, burglary, robbery, aggravated rape, or arson.” Tex. Penal Code Ann. § 19.03(a)(2) (1974).
  As set forth in Texas law, the three special issues were:
  “(1) whether the conduct of the defendant that caused the death of the deceased was committed deliberately and with the reasonable expectation that the death of the deceased or another would result;
  “(2) whether there is a probability that the defendant would commit criminal acts of violence that would constitute a continuing threat to society; and
  “(3) if raised by the evidence, whether the conduct of the defendant in killing the deceased was unreasonable in response to the provocation, if any, by the deceased.” Tex. Code Crim. Proc. Ann., Arts. 37.071(b)(lM3) (Vernon Supp. 1980).
  Banks, in fact, had no criminal record at all. App. 255, ¶ 115; App. to • Pet. for Cert. C23. He also “had no history of violence or alcohol abuse and seemed to possess a self-control that would suggest no particular risk of future violence.” Ibid.
  Brady v. Maryland, 373 U. S. 83, 87 (1963), held that “the suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution.”
  Banks also alleged ineffective assistance of counsel at both the guilt and penalty phases; insufficient evidence on the second penalty-phase special issue (Banks’s propensity to commit violent criminal acts); and the exclusion of minority jurors in violation of Swain v. Alabama, 380 U. S. 202 (1965). App. to Pet. for Cert. C5-C7. Banks filed two further state postconviction motions; both were denied. Brief for Respondent 6-7, nn. 6 and 7 (citing Ex parte Banks, No. 13568-03 (Tex. Crim. App. 1993) (per curiam), and Ex parte Banks, No. 13568-06 (Tex. Crim. App.), cert. denied, 538 U. S. 990 (2003)).
  We hereinafter refer to these claims as the Farr Brady and Cook Brady claims respectively. See supra, at 682, n. 5.
  Federal Rule of Civil Procedure 15(b) provides: “When issues not raised by the pleadings are tried by express or implied consent of the parties, they shall be treated in all respects as if they had been raised in the pleadings. Such amendment of the pleadings as may be necessary to cause them to conform to the evidence and to raise these issues may be made upon motion of any party at any time ....” Rule 11 of the Rules Governing Section 2254 Cases in the United States District Courts provides that the Federal Rules of Civil Procedure apply “to the extent that they are not inconsistent with [habeas] rules.”
  The Fifth Circuit noted correctly that under Lindh v. Murphy, 521 U. S. 320, 336-337 (1997), the standards of the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), 110 Stat. 1214, do not apply to Banks’s petition. See App. to Pet. for Cert. A14-A15.
  Our disposition of the Farr Brady claim, and our conclusion that a writ of habeas corpus should issue with respect to the death sentence, render it unnecessary to address Banks’s claim of ineffective assistance of counsel at the penalty phase; any relief he could obtain on that claim would be cumulative.
  Banks’s federal habeas petition, the Court of Appeals said, stated a claim, only under Brady, that material exculpatory or impeachment evidence had been suppressed, not a claim under Napue v. Illinois, 360 U. S. 264 (1959), and Giglio v. United States, 405 U. S. 150 (1972), that the prosecution had failed to correct Farr’s false testimony. App. to Pet. for Cert. A29-A32; App. 259-260. In its view, the Court of Appeals explained, a Brady claim is distinct from a Giglio claim, App. to Pet. for Cert. A30; thus the two did not fit under one umbrella. But cf. United States v. Bagley, 473 U. S. 667, 679-680, n. 8 (1985); United States v. Agurs, 427 U. S. 97,103-104 (1976). On brief, the parties debate the issue. Brief for Petitioner 23-25; Brief for Respondent 21-22, n. 21. Because we conclude that Banks qualifies for relief under Brady, we need not decide whether a Giglio claim, to warrant adjudication, must be separately pleaded. .
  Surprisingly, the Court of Appeals’ per curiam opinion did not refer to Strickler v. Greene, 527 U. S. 263 (1999), the controlling precedent on the issue of “cause.” App. to Pet. for Cert. A15-A33.
  We left open the question “whether any one or two of these factors would be sufficient to constitute cause.” Strickler, 527 U. S., at 289. We need not decide that question today.
  In addition, Banks could have expected disclosure of Farr’s informant status as a matter of state law if Farr in fact acted in that capacity. Under Texas law applicable at the time of Banks’s trial, the State had an obligation to disclose the identity of an informant when “the informant... was present at the time of the offense or arrest . . . [or] was otherwise shown to be a material witness to the transaction ....” Kemner v. State, 589 S. W. 2d 403, 408 (Tex. Crim. App. 1979) (quoting Carmouche v. State, 540 S. W. 2d 701, 703 (Tex. Crim. App. 1976)); cf. Tex. Rule Evid. 508(c)(1) (2003) (“No privilege exists [for the identity of an informer] ... if the informer appears as a witness for the public entity.”). Farr was present when Banks was arrested. App. 443, ¶ 10. Further, as the prosecution noted in its penalty-phase summation, Farr’s testimony was not only material, but “of the utmost significance.” Id., at 146.
  The Court of Appeals also stated that, because “the State did not respond” to Banks’s “Farr-was-an-informant contention” in its answer to the January 1992 state habeas application, Banks should have “further investigate!)!].” App. to Pet. for Cert. A22. The Fifth Circuit’s error in this regard is apparent. As earlier recounted, see supra, at 683, the State’s answer indeed did deny Banks’s allegation.
  Furthermore, rather than conceding the need for factual development of the Farr Brady claim in state postconviction court, the State asserted that Banks’s prosecutorial misconduct claims were meritless and procedurally barred in that tribunal. App. 234, 240. Having taken that position in 1992, the State can hardly fault Banks now for failing earlier to request assistance the State certainly would have opposed.
  It bears reiteration here that Banks had no criminal record, id., at 255, ¶ 115, “no history of violence or alcohol abuse,” nothing indicative of “[any] particular risk of future violence,” App. to Pet. for Cert. C23.
  It also appears that the remaining prosecution witness in the penalty phase, Vetrano Jefferson, had omitted crucial details from his 1980 testimony. In his September 1980 testimony, Vetrano Jefferson said that Banks had struck him with a pistol in early April 1980. App. 104-105; supra, at 679-680. In the federal habeas proceeding, Vetrano Jefferson elaborated that he, not Banks, had initiated that incident by making “disrespectful comments” about Demetra Jefferson, Banks’s girlfriend. App. 337, ¶ 4. Vetrano Jefferson recounted that he “grew angry” when Banks objected to the comments, and only then did a fight ensue, in the course of which Banks struck Vetrano Jefferson. Ibid.
  On brief and at oral argument, the State suggests that “the damaging evidence was Banks’s willing abetment of Farr’s commission of a violent crime, not Banks’s own intent to commit such an act.” Brief for Respondent 25 (emphasis in original); Tr. of Oral Arg. 50. See also post, at 707-708 (Thomas, J., concurring in part and dissenting in part). In the penalty-phase summation, however, the prosecution highlighted Banks’s propensity to commit violent criminal acts, see App. 140, 144, 146-147, not his facilitation of others’ criminal acts, see id, at 141 (“[Banks] says, T thought I would give [the gun] to them so they could do the robberies.’ I don’t believe you [the jury] believe that.”); id, at 143 (“a man doesn’t travel two hundred miles ... to supply [another] person with a weapon”). The special issue the prosecution addressed focused on what acts Banks would commit, not what harms he might facilitate: “Do you find from the evidence beyond a reasonable doubt that there is a probability that the defendant, Delma Banks, Jr., would commit criminal acts of violence that would constitute a continuing threat to society?” Ibid, (internal quotation marks omitted and emphasis added). It is therefore unsurprising that the prosecution did not rest on Banks’s facilitation of others’ criminal acts in urging the jury to answer the second special issue (propensity to commit violent criminal acts) in the affirmative.
  See Federal Evidentiary Hearing 56-73. Examining one of Banks’s prosecutors, counsel for Banks twice asked if Cook had been “instructed ... on how to testify.” Id., at 56, See also id., at 63-64 (“Texarkana law enforcement did not instruct Mr. Cook how to testify in this case. Is that your testimony today?”). To show that Cook had been coached, Banks’s counsel called attention to discrepancies between portions of the September 1980 transcript and Cook’s trial testimony. Id., at 65-68. Concluding his examination, Banks’s counsel emphasized the prosecution’s duty to disclose the September 1980 transcript once Cook, while on the stand, stated that he had not been coached. Id., at 73-74; App. 59; supra, at 677.
  Banks’s case provides no occasion to consider Rule 15(b)’s application under the AEDPA regime.
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