
495 F.3d 873 (2007)
UNITED STATES of America, Appellee,
v.
Michael R. BURNS, Appellant.
No. 06-3820.
United States Court of Appeals, Eighth Circuit.
Submitted: June 14, 2007.
Filed: August 1, 2007.
Rehearing and Rehearing Denied August 31, 2007.
*874 John R. Osgood, Lee's Summit, MO, argued for appellant.
Philip M. Koppe, Asst. U.S. Atty., Kansas City, MO, argued (Bradley J. Schlozman, U.S. Atty., on the brief), for appellee.
Before LOKEN, Chief Judge, ARNOLD and COLLOTON, Circuit Judges.
Rehearing and Rehearing En Banc Denied August 31, 2007.
ARNOLD, Circuit Judge.
A jury convicted Michael Burns of one count of conspiring to distribute 500 grams or more of methamphetamine, see 21 U.S.C. §§ 841(a)(1), (b)(1)(A), 846, and two counts of distributing 50 grams or more of the drug, see 21 U.S.C. § 841(a)(1), (b)(1)(B). After the district court[1] imposed a sentence of three concurrent terms of 360 months' imprisonment, we affirmed the conviction and remanded the case for resentencing. United States v. Burns, 432 F.3d 856 (8th Cir.2005). On remand, Mr. Burns moved for a new trial under Federal Rule of Criminal Procedure 33, and the district court denied the motion without an evidentiary hearing. Mr. Burns appeals and we affirm.

I.
Mr. Burns claims that newly discovered evidence shows that Missouri Highway Patrol chemist Matthew Barb perjured himself when he testified at trial about the quantity of drugs put in evidence against Mr. Burns. After Mr. Burns's trial, investigators discovered that Mr. Barb was a drug addict who had been pilfering drugs from lab samples, and Mr. Barb later pleaded guilty to stealing amphetamines from the Highway Patrol lab where he worked. Mr. Burns thus speculates that Mr. Barb may have tampered with the evidence that was introduced at Mr. Burns's trial and contends that the revelations about Mr. Barb's activities entitle him to a new trial.
Mr. Burns maintains first that he is entitled to a new trial because Mr. Barb's testimony tainted his original trial. As support for this contention, Mr. Burns relies on Mesarosh v. United States, 352 U.S. 1, 77 S.Ct. 1, 1 L.Ed.2d 1 (1956). Mesarosh did not involve a new trial motion: While that case was pending in the Supreme Court, the government itself brought to the Court's attention new evidence showing that a crucial government witness who had testified against the criminal defendant had not told the truth in numerous other proceedings against other individuals in which he had testified "in the same field of activity," i.e., as a government informant paid to infiltrate the Communist Party. Id. at 4-8, 10, 77 S.Ct. 1. Relying on its supervisory authority over lower federal courts, the Court held that the defendant was entitled to a new trial because the witness's repeated untruthfulness *875 (whether deliberate or the result of a psychiatric condition) had "tainted" the defendant's conviction. Id. at 9, 14, 77 S.Ct. 1.
The Mesarosh holding has no application to the present case because there is no evidence whatever that Mr. Barb was a practiced perjurer or suffered from some disqualifying mental condition. There was, moreover, no evidence that he perjured himself in Mr. Burns's trial. The worst that might be said with any confidence about Mr. Barb's testimony is that he did not disclose his drug habit or his thefts. But a failure to disclose matter that might be useful for impeachment purposes is not perjury. Mr. Burns offers no evidence that contradicts any particular answer that Mr. Barb gave at trial. We thus have no reason to believe that Mr. Burns's trial was tainted in the way that the trial in Mesarosh was. The newly discovered information about Mr. Barb's criminal activities could have been used to impeach his general credibility, but that is a different matter entirely.

II.
Mr. Burns also contends that he should get a new trial because of newly discovered evidence. To be eligible for a new trial on this basis, he must establish, among other things, that the new evidence "would likely produce an acquittal." United States v. Barajas, 474 F.3d 1023, 1026 (8th Cir.2007). Here, the new evidence is admissible only for impeachment purposes, and this kind of evidence is rarely sufficient to entitle a defendant to a new trial. See Mesarosh, 352 U.S. at 9, 77 S.Ct. 1. We see no reason to think that the impeachment evidence would have produced an acquittal on any count or a jury finding that the conspiracy involved less than 500 grams of methamphetamine or that the distribution counts were based on the transfer of less than 50 grams of drugs.
The case against Mr. Burns, including the amount of drugs with which he was involved, was overwhelming, and it suffices to mention here only some of the most incriminating evidence against him. On two occasions, Mr. Burns negotiated with an undercover officer and sold the officer an ounce of methamphetamine each time. Other witnesses testified that Mr. Burns was involved in a conspiracy to sell methamphetamine: one of them, co-defendant Howard Neustel, testified in detail about Mr. Burns's criminal activities and kept ledgers recording the large amounts of methamphetamine that he bought from Mr. Burns and the sums that he paid for them. Mr. Burns does not dispute that methamphetamine was seized from him and his criminal associates. We note, moreover, that if Mr. Barb stole methamphetamine from the drugs relevant to Mr. Burns's case, that could only have reduced, not increased, the amount of drugs attributable to him.

III.
Mr. Burns offered the district court an affidavit from juror Patricia Kassab as evidence that she would have voted to acquit him had the newly discovered evidence been introduced at trial. In her affidavit, Ms. Kassab attested that had she known during the trial about Mr. Barb's drug addiction and theft "it would have caused [her] reasonable doubt as to the proof of the amount and weight of the methamphetamine offered into evidence in Mr. Burns's case."
Federal Rule of Evidence 606(b) generally prohibits a juror from testifying about her or other jurors' mental processes during jury deliberations. We think that the principle behind this prohibition extends to testimony about what those mental processes would have been had the evidence at trial been different. Cf. Capps v. Sullivan, *876 921 F.2d 260, 262-63 (10th Cir.1990). More fundamentally, the question of whether different evidence would have produced a different result must be answered by asking what a reasonable jury would likely have done with that evidence before it, not what some particular juror or jurors would have done. We therefore decline to give Ms. Kassab's affidavit any weight.

IV.
Mr. Burns also contends that the district court should have given him an evidentiary hearing before making a decision on his motion for a new trial. When ruling on a new trial motion based on newly discovered evidence, the "district court has broad discretion in deciding whether an evidentiary hearing is necessary." United States v. Provost, 969 F.2d 617, 619 (8th Cir.1992), cert. denied, 506 U.S. 1056, 113 S.Ct. 986, 122 L.Ed.2d 139 (1993). We hold that the district court did not abuse its discretion here because Mr. Burns failed to show that his case involved any "exceptional circumstances" that might have required a hearing. See id. Indeed, Mr. Burns never established how a hearing was at all likely to produce the type of evidence that would entitle him to a new trial.
Affirmed.
NOTES
[1]  The Honorable Richard E. Dorr, United States District Judge for the Western District of Missouri.
