The United States Supreme Court remanded this case to this court for a determination of whether the government’s failure to disclose material impeachment evidence to defendant Hughes Anderson Bagley prior to trial “undermines confidence in the outcome of the trial,” requiring reversal of Bagley’s conviction. United States v. Bagley, — U.S. —, 105 S.Ct. 3375, 3381 , 87 L.Ed.2d 481 (1985). We determine that it does, and reverse.

I.

In October 1977, a federal grand jury indicted Bagley on firearms and controlled substance violations. After a bench trial in December 1977, the district court acquitted him on the firearms charges and convicted him of the controlled substance violations.

A month before trial, Bagley requested that the government disclose, pursuant to Brady v. Maryland, 373 U.S. 83 , 83 S.Ct. 1194 , 10 L.Ed.2d 215 (1963), exculpatory or impeachment information in its possession. Bagley requested information on

The government responded by stating that it already had provided extensive discovery, including affidavits of two government witnesses acquainted with Bagley: James F. O’Connor and Donald E. Mitchell, special agents for Milwaukee Railroad who had assisted the Bureau of Alcohol, Tobacco & Firearms (ATF) investigation of Bagley. The affidavits recounted the agents’ interactions with Bagley. Each affidavit stated: “I made this statement freely and voluntarily without any threats or rewards, or promises of reward having been made to me in return for it.”

At trial O’Connor and Mitchell provided the only testimony on the controlled substance charges. Bagley’s cross-examination of the two on the controlled substance charges sought only to refute their substantive testimony. After O’Connor denied on cross-examination that the government pressured him in any way or made threats that his job would be jeopardized if he did not cooperate, Bagley did not pursue the issue of bias or self-interest with O’Connor or Mitchell.

Three years after his conviction, Bagley learned that O’Connor and Mitchell lied under oath when they stated in their affidavits that they had not been promised any reward for their cooperation. In fact, they were acting under inducements from the federal government. Six months before Bagley’s trial, ATF paid O’Connor and Mitchell expense money for their part in the investigation of Bagley. ATF Agent Prin also told them he would try to obtain further compensation for them. The day before O’Connor and Mitchell signed the last of the affidavits disclaiming any promise of reward for their services, Agent Prin had each sign an ATF “Contract for Purchase of Information and Lump Sum Therefor.” Agent Prin had not filled in the amount to be paid, or the specific information requested, but the contract stated that

After trial, Agent Prin typed in the following description of the services:

He recommended that O’Connor and Mitchell each receive $500 for their services; they each received $300. The government disclosed these contracts three years after trial, only when Bagley filed a request for information under the Freedom of Information Act and Privacy Act of 1974, 5 U.S.C. §§ 552 , 552a.

When Bagley learned that, despite his requests for impeachment evidence before trial, the government had failed to produce evidence of the payments and inducements made to the witnesses, he filed a 28 U.S.C. § 2255 motion in federal district court. Bagley argued that the government violated his due process rights under Brady by failing to produce evidence material to the witnesses’ credibility.

After an evidentiary hearing, a United States magistrate recommended to the district court that it deny Bagley’s motion. The district court judge was the same judge who conducted the bench trial and imposed sentence. In its order denying relief, the district court stated that it was “in a unique position of being able to know what effect the disclosure ... would have had upon the decisions made by this Court in the criminal prosecution.” He concluded that “disclosure would have had no effect at all upon its finding that the government had proved beyond a reasonable doubt that defendant was guilty.”

We reversed the district court. Bagley v. Lumpkin, 719 F.2d 1462 (9th Cir.1983), rev’d, — U.S. —, 105 S.Ct. 3375 , 87 L.Ed.2d 481 (1985). We held that “the government’s failure to provide requested Brady information to Bagley so that he could effectively cross-examine two impor tant government witnesses requires an automatic reversal.” Id. at 1464.

The Supreme Court reversed our ruling that automatic reversal was required, and remanded to this court for us to determine whether the government’s inducements to O’Connor and Mitchell, evidenced by the ATF contracts, were sufficiently material that there was a reasonable probability that “the result of the proceeding would have been different.” United States v. Bagley, — U.S.—, 105 S.Ct. 3375, 3384 , 87 L.Ed.2d 481 (1985).

II.

Bagley contends that the government’s withholding of evidence was sufficiently material that his conviction should be reversed. He argues, therefore, that the district court erred in denying his section 2255 motion. We review de novo the district court’s denial of a section 2255 motion. Jones v. United States, 783 F.2d 1477, 1479 (9th Cir.1986).

Every prosecutor has a duty to produce, on request by the defendant, evidence that is material to the defendant’s guilt or punishment. Brady v. Maryland, 373 U.S. 83, 87 , 83 S.Ct. 1194, 1196 , 10 L.Ed.2d 215 (1963). This obligation includes production of impeachment evidence. Bagley, 105 S.Ct. at 3381 (“ ‘When the “reliability of a given witness may well be determinative of guilt or innocence,” nondisclosure of evidence affecting credibility falls within the general rule [of Brady ].’ ”) (quoting Giglio v. United States, 405 U.S. 150, 154 , 92 S.Ct. 763, 766 , 31 L.Ed.2d 104 (1972)). Withholding such evidence is a constitutional error if it deprives a defendant of a fair trial. Id.; see also Brady, 373 U.S. at 87 , 83 S.Ct. at 1196 (“[0]ur system of the administration of justice suffers when any accused is treated unfairly.”). In Bagley the Supreme Court held that “a constitutional error occurs, and the conviction must be reversed, only if the evidence is material in the sense that its suppression undermines confidence in the outcome of the trial.” Bagley, 105 S.Ct. at 3381 ; see also United States v. Shaffer, 789 F.2d 682, 688 (9th Cir.1986).

To determine whether the impeachment evidence withheld here was sufficiently material to require reversal of Bagley’s conviction, we must evaluate whether, “if disclosed and used effectively, [the impeachment evidence] may make the difference between conviction and acquittal.” Bagley, 105 S.Ct. at 3380 (citing Napue v. Illinois, 360 U.S. 264, 269 , 79 S.Ct. 1173, 1177 , 3 L.Ed.2d 1217 (1959)). Our task is to “consider directly any adverse effect that the prosecutor’s failure to respond might have had on the preparation or presentation of the defendant’s case,” and to assess that effect “in light of the totality of the circumstances.” Id. 105 S.Ct. at 3384 .

The proper inquiry is an objective one: whether “the Government’s failure to assist the defense by disclosing information that might have been helpful in conducting cross-examination” undermines confidence in the outcome of the trial. Id. at 3381 . Therefore, the district judge erred when, in ruling on the section 2255 motion, he stated that the disclosure of the contracts would not have affected his decision. The inquiry is not how this or any other judge, as the trier of fact, would subjectively evaluate the evidence. It is, rather, how the absence of the evidence objectively might have affected the outcome of the trial.

The district court further erred by failing to recognize that the ATF contracts revealed that the witnesses lied under oath. The district court’s findings of fact in this action take into account only the extent to which the contracts demonstrate possible bias or prejudice. It is inconceivable that evidence of perjury would not, as an objective matter, affect a factfinder’s assessment of a witness’ credibility. When the evidence shows that the government’s only witnesses lied under oath,- it is contrary to reason that confidence in the outcome of the case would not objectively be undermined. See Shaffer, 789 F.2d at 689 (new trial required because government withheld material evidence that contradicted key witness’ testimony as well as evidence tending to show it paid same witness for his cooperation). This is particularly true here because the lies came from the only witnesses who testified against Bagley and the lies related to the reasons why they testified. Evidence of bias and prejudice is certainly material for impeachment, but lies under oath to conceal bias and prejudice raise the impeachment evidence to such a level that it is difficult to imagine anything of greater magnitude that would undermine confidence in the outcome of any trial.

Producing the ATF contracts “might have been helpful,” Bagley, 105 S.Ct. at 3381 , for defense counsel’s preparation and presentation of Bagley’s case. The government’s case rested solely on the credibility of O’Connor and Mitchell. Both testified that Bagley gave them controlled substances; the only corroborating evidence for each came from the other. We recognize that, under certain circumstances, the failure to disclose a government inducement made to a witness may not require reversal. See United States v. Pflaumer, 774 F.2d 1224, 1230-31 (3d Cir.1985) cert. denied, — U.S. —, 106 S.Ct. 1263 , 89 L.Ed.2d 572 (1986). In Pflaumer , the failure to disclose a promise of use immunity given to one of several witnesses was not “material” because his testimony was merely cumulative and substantial other direct and circumstantial evidence implicated the defendant. Id. at 1229-30 . But, when the witnesses’ testimony is central to the government’s case, their credibility is “an important issue in the case.” Giglio, 405 U.S. at 155 , 92 S.Ct, at 766 ; see also Shaffer, 789 F.2d at 688-89 (because testimony implicating defendant critical to conviction, jury assessment of credibility crucial to trial outcome).

Accordingly, knowledge of the ATF contracts could have given Bagley an entirely different trial strategy that might have resulted in his acquittal. See Bagley, 105 S.Ct. at 3384 . Had the defendant known the government witnesses’ testimony could be impeached by showing bias or an incentive to testify falsely, he might not have waived his right to a jury trial. Counsel would not have been limited to planning a defense against the controlled substance charges based exclusively on substantive grounds. Counsel did not pursue his attempt to question O’Connor’s motivations when O’Connor denied that the government threatened his job if he did not cooperate. Nor did counsel inquire into Mitchell’s bias or self-interest. Counsel’s abandonment of this line of questioning makes sense in light of the affidavits. Counsel could have used the contracts to discredit all of O’Con-nor’s and Mitchell’s testimony. Evidence of potential payment would challenge the veracity both of their direct testimony and of their substantive cross-examination testimony. See United States v. Abel, 469 U.S. 45, 105 S.Ct. 465, 468 , 83 L.Ed.2d 450 (1984) (“A successful showing of bias on the part of a witness would have a tendency to make the facts to which he testified less probable in the eyes of the jury than it would be without such testimony.”). More important, counsel could have shown that the witnesses’ denials of inducements in their affidavits were a lie.

The contracts at issue in this case “bore directly not only on the fact of bias but also on the source and strength of [the witness’] bias.” Abel, 105 S.Ct. at 470 (emphasis omitted). These contracts plainly stated that “upon the accomplishment of the objective sought to be obtained” to the ATF’s satisfaction, O’Connor and Mitchell would be paid “commensurate with services and information rendered.” These contractual terms were inconsistent with the disclaimers in the affidavits and compromised O’Connor’s and Mitchell’s ability to and interest in testifying fairly. As Justice Blackmun observed:

Bagley, 105 S.Ct. at 3384 ; see also Boone v. Paderick, 541 F.2d 447, 451 (4th Cir. 1976) (“[T]he more uncertain the agreement, the greater the incentive to make the testimony pleasing to the promisor.”), cert. denied, 430 U.S. 959 , 97 S.Ct. 1610 , 51 L.Ed.2d 811 (1977); cf. Haber v. Wainwright, 756 F.2d 1520, 1524 (11th Cir.1985) (even mere advice to key witness that state would not prosecute in exchange for testimony may be informal understanding directly affecting witness credibility).

As the foregoing discussion demonstrates, the government’s failure to disclose the contracts to Bagley unconstitutionally “deprive[d] the defendant of a fair trial.” Bagley, 105 S.Ct. at 3381 . Accordingly, we conclude that the nondisclosure of this Brady material “undermines [our] confidence in the outcome of [Bagley’s] trial.” Id.

The effect of the government’s failure to produce the contracts for Bagley before trial was compounded by its presentation of the affidavits disclaiming any promises or inducements. Bagley’s specific request for “all documents ... [containing] promises or representations made to any ... witnesses” imposed on the prosecution a duty to obtain all material documents. By providing the affidavits that disclaimed any threats, rewards, or promises of rewards, the government made an affirmative representation that no such documents existed. This assertion perpetuated the lie that O’Connor and Mitchell were not acting under inducements.

III.

By failing to produce the inducements made to its two witnesses, who supplied the only evidence to convict Bagley, the government unconstitutionally interfered with Bagley’s right to a fair trial. Therefore, the government’s Brady error undermines confidence in the outcome of Bagley’s trial and requires reversal of his conviction.

REVERSED AND REMANDED WITH INSTRUCTION^ TO VACATE BAGLEY’S SENTENCE.

. There was no corroborating evidence. O’Con-nor and Mitchell taped their meetings with Bagley, but the district court refused to admit the tapes into evidence because they were only partially audible. . We read the Supreme Court’s instruction to us in this case that we determine whether there was a reasonable probability that the result of the trial would have been different in conjunction with their admonition that to constitute reversible error the failure to disclose Brady material must undermine the confidence in the outcome of the trial. In this case, a unanimous panel of three former trial judges find that the kind of information not disclosed in this case was significant. Moreover, we find that the non-disclosed Brady material was of such significance that it creates doubt in our minds as to whether the result of this trial would have been different. For the reasons set forth more fully in the text of the opinion, we believe that the doubt created in our minds as to whether the result would have been different in this case ' had the information been disclosed satisfies the reasonable probability standard enunciated by the Supreme Court. . The constitutional error in this case was committed by the government and not by the court. Bagley, 105 S.Ct. at 3381 . Therefore, cases that discuss standards for reviewing judicial limitations on the use of bias evidence at trial do not apply to Brady violations. See, e.g., Delaware v. Van Arsdall, — U.S.—, 106 S.Ct. 1431, 1438 , 89 L.Ed.2d 674 (1986) (prohibiting defense counsel from attempting to impeach a government witness for bias subject to harmless-error analysis). . In Reiger v. Christensen, 789 F.2d 1425, 1432 (9th Cir.1986), we stated that" ‘evidence is material only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.’" (quoting Bagley, 105 S.Ct. at 3384 ). "A ‘reasonable probability’ is a probability sufficient to undermine confidence in the outcome.” Bagley, 105 S.Ct. at 3384 .