208 F.3d 662 (8th Cir. 2000)
WILLIAM FRANCIS DYE, APPELLANT,v.LOUIS A. STENDER, WARDEN, APPELLEE.
No. 98-2040
UNITED STATES COURT OF APPEALS FOR THE EIGHTH CIRCUIT
Submitted: November 19, 1999Filed: March 23, 2000

Appeal from the United States District Court for the District of Minnesota.[Copyrighted Material Omitted]
Before Wollman, Chief Judge, Lay, and Hansen, Circuit Judges.
Wollman, Chief Judge.


1
William F. Dye appeals from the district court's1 denial of a writ of habeas corpus under 28 U.S.C. § 2254 on his claim that two witnesses at his state murder trial had undisclosed deals with the government. We affirm.

I.

2
On September 29, 1981, a jury convicted Dye of second-degree murder for the fatal shooting of the assistant manager of a St. Paul pizzeria during a robbery attempt. The evidence linking Dye to the offense was characterized by the Supreme Court of Minnesota as "so strong that it would serve no useful purpose to summarize it . . . ." State v. Dye, 333 N.W.2d 642, 643 (Minn. 1983). Along with the two witnesses whose testimony is in question, the State's evidence included the testimony of the three pizzeria employees who were present during the shooting and of numerous police agents involved in the surveillance of Dye when he disposed of what was determined to be the murder weapon. After his conviction and sentencing to 298 months' imprisonment, Dye sought relief from the state courts. His claims were denied on appeal and in four state post-conviction relief proceedings.


3
The two individuals whose testimony Dye challenges in this appeal are Deck Brewer, an inmate who had had contact with Dye in jail during the time preceding Dye's trial, and Frank Kranz, an acquaintance who, at the time of Dye's arrest, had pled guilty to federal charges and was awaiting sentencing. Dye contends that undisclosed deals that Kranz and Brewer made with state and federal officials violated his right to the disclosure of material evidence established by Brady v. Maryland, 373 U.S. 83, 87 (1963). Dye offers in support of this argument two letters written by government officials on Kranz's behalf four months before Dye's trial, together with testimony from Brewer's sentencing hearing, which occurred approximately a month after Dye's trial. Dye also contends that the State's knowing use of the witnesses' testimony that there were no deals violates the rule of Napue v. Illinois, which forbids a prosecutor to allow false testimony to go uncorrected. See 360 U.S. 264, 269-70 (1959).


4
In response to Dye's third petition for post-conviction relief, the state court explicitly stated that there was no evidence that suggested that either Kranz or Brewer had had a deal or had been compensated for testifying against Dye. See Appellee's App. at 32-35 (Dye v. State, Minn. Dist. Ct. Order and Mem. of Feb. 12, 1993 (unpublished)). In affirming this denial of relief, which also denied an evidentiary hearing on the matter, the Minnesota Court of Appeals held that regardless of whether the letters should have been disclosed, Dye could not succeed on his Napue claim because there was no reasonable likelihood that any allegedly false testimony affected the jury and that, under Brady, Dye could not succeed because the alleged non-disclosure was "immaterial in light of the other evidence." See Appellee's App. at 38 (Dye v. State, Minn. Ct. App. Order Op. of Aug. 10, 1993) (unpublished)).


5
Dye then filed a petition for habeas corpus in federal court. After examining the record, a magistrate judge issued a report and a recommendation that Dye's petition be denied. The magistrate judge found no error in the state courts' conclusion that there was no evidence of a deal for either witness. The magistrate also agreed that even if such evidence had existed, Brady would not have required its disclosure nor would it have changed the outcome or been "anything but harmless" under Napue. See Appellee's App. at 13-16, 20-21 (Dye v. Stender, Report and Recommendation of June 3, 1997). After conducting a de novo review, the district court adopted the magistrate judge's report and recommendation and dismissed Dye's petition.


6
We granted a certificate of appealability on Dye's claims concerning Kranz and Brewer.

II.
A. Standard of Review

7
Whether the State made deals with Kranz and Brewer is a factual question, entitled to a presumption of correctness unless the petitioner can clearly and convincingly show otherwise. See Blair v. Armontrout, 916 F.2d 1310, 1318 (8th Cir. 1990) (existence of deals is factual question); 28 U.S.C. § 2254(e)(1) (1999) (presumption of correctness); Richardson v. Bowersox, 188 F.3d 973, 977 (8th Cir. 1999) (same presumption). We review the district court's findings of fact for clear error and its conclusions of law de novo. See Richardson, 188 F.3d at 977.


8
Dye filed his petition for habeas corpus relief on October 15, 1996, so we apply the standards of the Antiterrorism and Effective Death Penalty Act of 1996. Pub. L. No. 104-132, 110 Stat. 1214 (April 24, 1996) (AEDPA). "We may grant the writ only if the state court's adjudication of the claims 'resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court,'" Lingle v. Iowa, 195 F.3d 1023, 1025 (8th Cir. 1999) (quoting 28 U.S.C. § 2254(d)(1) (1999)), or if the state court's adjudication "resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(2) (1999).

B. Evidence of a Deal

9
The interest of the government "in any criminal prosecution 'is not that it shall win a case, but that justice shall be done.'" Lingle, 195 F.3d at 1026 (quoting Berger v. United States, 295 U.S. 78, 88 (1935)). "For this reason . . . the prosecution is required to divulge all evidence favorable to the accused that is material either to guilt or to punishment," a rule known as the Brady rule. Id.; see Brady, 373 U.S. at 87. Evidence that "impeach[es] the credibility of a government witness . . . falls under the Brady doctrine." United States v. O'Conner, 64 F.3d 355, 358 (8th Cir. 1995). To establish a violation of Brady, a defendant must show that: (1) the prosecution suppressed evidence, (2) the evidence was favorable to the accused, and (3) the evidence was material. See Johns v. Bowersox, 203 F.3d 538, 545 (8th Cir.2000). A Brady violation will not necessarily result in reversal of the conviction if it was "not prejudicial and amount[s] to harmless error." United States v. Williams, 194 F.3d 886, 889 (8th Cir. 1999).

1. Kranz's Testimony

10
Kranz testified at Dye's trial that he had been offered no deals or promises by state or federal officials at any time. Dye points out that both an assistant county attorney and an assistant United States attorney wrote letters in July of 1981 describing Kranz's cooperation in the murder investigation. Dye contends that these letters, which were not disclosed to Dye until after his conviction, are evidence of inducement for Kranz to testify against him and that even if they were unrelated to Kranz's trial testimony, they still constitute evidence that Kranz had had a deal with the government, and thus raise an inference that Kranz likely had another agreement for his testimony.


11
We find no clear error in the district court's finding that Kranz did not have a deal and that Dye did not successfully rebut the presumption of the correctness of the state court's determination. The letters written on Kranz's behalf stressed his voluntary cooperation in helping to solve the murder and only mention the probability that he would testify at Dye's trial. Kranz had pled guilty to federal charges before the pizzeria murder occurred and was sentenced approximately a week after Dye's arrest, months before the letters were written. That Kranz moved for a reduction in his federal sentence a month before Dye's trial and may have used the letters as support does not clearly and convincingly belie the proposition that the government had no arrangements with Kranz, either during the investigation or during Dye's trial. The state court that heard Dye's third petition noted that such sentence reduction motions are routinely filed and that the sentence Kranz ultimately received was entirely within the discretion of the federal judge. Kranz may certainly have hoped that his cooperation with authorities in solving the crime would help him, but the letters do not present clear, convincing evidence of an inducement. Accordingly, we cannot say that the district court clearly erred in finding that no deals had been made.

2. Brewer's Testimony

12
Brewer testified that state officials had not given him any promises or deals. At Brewer's sentencing hearing on November 4, 1981, more than a month after Dye's trial, Brewer's attorney mentioned Brewer's Dye-trial testimony during a discussion of a plea bargain. Dye points to this as evidence that Brewer's testimony at Dye's trial was given pursuant to a deal, the existence of which should have been disclosed.


13
The state courts noted that it was likely that Brewer's "deal," if he had one, was to plead guilty to a superseding indictment in exchange for a lesser sentence. There is evidence that Brewer had hoped to gain a sentence reduction by testifying against Dye, bragging about this possibility within the jail confines (evidence of which was presented at Dye's trial), but we cannot say that the testimony at his federal sentencing hearing conclusively shows that he had an arrangement with the government relating to this testimony. Accordingly, we find no clear error in the district court's finding that Brewer had no deal with the state.

3. Materiality

14
Assuming for the purpose of argument that Kranz and Brewer had entered into deals with the government in exchange for their testimony, we conclude that evidence thereof would not be material under Brady. Evidence is considered material when a reasonable probability exists that, "had the evidence been disclosed to the defense, the result of the proceeding would have been different." O'Conner, 64 F.3d at 358 (quoting United States v. Bagley, 473 U.S. 667, 682 (1985)). A reasonable probability is "a probability sufficient to undermine confidence in the outcome." Id.


15
Dye argues that Kranz and Brewer were crucial witnesses and that the evidence of their arrangements with the government would have been important in gauging their credibility. Kranz testified about a "dry run" of the pizzeria robbery, which he took with Dye before the murder occurred. He also identified the murder weapon as belonging to Dye. Brewer testified to Dye's comments in jail about the murder charges, comments that provided an explanation on the issue of intent and which suggested that Dye manufactured an alibi after his arrest. Brewer also provided an explanation for several of Dye's actions that would have otherwise seemed rather counterintuitive, such as his retaining the murder weapon after disposing of other incriminating evidence.


16
We believe that in light of the overwhelming circumstantial evidence of Dye's guilt, any additional evidence of Kranz's and Brewer's lack of credibility would have been immaterial. Dye matched the general physical description of the robber given by eye-witnesses, he attempted to dispose of the murder weapon, he owned a pair of gloves that were determined to likely have been used in the recent firing of a gun, and he attempted to dispose of a mask similar to that worn by the robber. The testimony of many police officers, of the eye-witnesses, and of forensic experts linked Dye to the crime and corroborated Brewer's and Kranz's testimony. Kranz and Brewer were subjected to extensive cross-examination regarding their felony convictions. Kranz was questioned about his agreement with state officials to tape record telephone conversations with Dye. These conversations were orchestrated to provide incriminating evidence against Dye; the recordings were ultimately played at trial by defense counsel. The defense also presented the testimony of several prisoners who described the animosity between Brewer and Dye and how Brewer encouraged other inmates to testify against Dye, boasting that his testimony was going to earn him a sentence reduction and that their testimony could do the same for them.


17
In light of the evidence, our confidence in the verdict is not undermined, and therefore we conclude that Dye's claim must fail.

C. Perjured Testimony Under Napue

18
Because we find no clear error in the factual determination that there were no secret deals with Kranz and Brewer, and thus that neither witness perjured himself on that topic, we need not address Dye's Napue claims. Moreover, for the same reasons that our confidence in the verdict is not undermined in the Brady context, we do not believe Dye could successfully show a reasonable likelihood that the jury would have been affected by any of the false testimony, a necessary component of a Napue claim.


19
The judgment is affirmed.



NOTE:


1
  The Honorable John R. Tunheim, United States District Judge for the District of Minnesota, adopting the recommendation and report of the Honorable John M. Mason, United States Magistrate Judge for the District of Minnesota.


