James Johnson and Ozem Thomas appeal from judgments of conviction entered following a jury trial in the United States District Court for the Eastern District of New York (Korman, Ch.J.). Defendants, who are African-American, argue principally that the prosecutor violated the 'equal protection principle of Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), when he exercised peremptory challenges to strike two prospective jurors who are also African-American. In United States v. Thomas (“Thomas I”), 303 F.3d 138 (2d Cir.2002), we held that the factual findings made by the magistrate judge who oversaw jury selection were insufficient to support denial of defendants’ Batson motions. We remanded for supplemental findings pursuant to the procedure used in United States v. Jacobson, 15 F.3d 19, 21-22 (2d Cir.1994). See Thomas I, 303 F.3d at 146-47. Now, having reviewed the findings made on remand, we vacate defendants’ convictions and remand for a new trial.
Ozem Thomas and James Johnson were tried on numerous counts arising out of four robberies or attempted robberies in Brooklyn. Upon consent, Magistrate Judge Simon A. Chrein presided over jury selection, during which the government used its peremptory challenges to strike one person of Latino ancestry and four African-Americans. Our decision in Thomas I concerned the prosecution’s strike of two African-American jurors: Emma Franklin and Dorothy Campbell. See 303 F.3d at 140-142,144-46.
I
Under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69, a trial court must engage in “a three-step[ ] burden-shifting analysis to determine whether a peremptory strike has been exercised in a racially discriminatory manner.” Barnes v. Anderson, 202 F.3d 150, 155 (2d Cir.1999). First, the court must ask “whether the movant has made a pri-ma facie showing that the non-movant has exercised its peremptory strike on the ba*317sis of race.” Id. (internal quotation marks and alterations omitted). Second, the court must determine whether the non-movant has provided a facially non-discriminatory reason for exercising the strike. Purkett v. Elem, 514 U.S. 765, 767-68, 115 S.Ct. 1769, 131 L.Ed.2d 834 (1995) (per curiam); Barnes, 202 F.3d at 155-56. Third, the court must determine whether the movant (with whom the burden of persuasion remains throughout the Batson analysis) has proved intentional or purposeful race discrimination. Barnes, 202 F.3d at 155-56. As in Thomas I, it is the third step of the Batson analysis that concerns us here.
II
Emma Franklin entered the jury box during the fifth round of voir dire. She stated that her son had been convicted on assault and weapons charges, and was currently in jail because he violated a five-year term of probation by being found in possession of a gun. Ms. Franklin stated that her son was treated fairly on the criminal charges, and she expressed relief that she could see her son, who “would have probably been dead otherwise.” Ms. Franklin expressed confidence that her son’s experiences with the criminal justice system “wouldn’t affect [her].” She was not challenged for cause.
The government did, however, exercise a peremptory challenge to remove her. The defense challenged the strike under Bat-son, and the government explained:
I would say this woman’s child is incarcerated on weapons charges, and this case involves two particular defendants who face — at least with respect to Ozem Thomas — face multiple weapons charges, and the defendant Johnson also faces a weapons charge.
So, there is a real similarity between the predicament, in terms of the weapon charge, I expect in this case, which I don’t expect in every case: That the defendants’ mothers are going to be a significant presence during the course of the trial.
And knowing that, and knowing that a mother also faces — is going to be seeing mothers in the audience who also have children, their children are incarcerated, it’s not a knee-jerk reaction just to the fact the child is incarcerated. But in this particular case, I expect the mothers to be a presence, and even to be witnesses in the case.
Thomas I, 303 F.3d at 140-41. The magistrate credited this explanation and denied the Batson motion.
The defense renewed its attack when the government decided in the following round not to strike a white juror, Ruby Leureux, whose son also had been convicted of a weapons offense. The defense argued:
Ms. Leureux had the same situation [as Ms. Franklin], She wasn’t challenged on that basis by the government as a peremptory. It’s exactly the same situation. She had a son who was arrested for a crime of robbery, I believe, with a weapon, and she is also a mother of a child. Her situation is exactly the same as Ms. Franklin’s. However, the government challenged Ms. Franklin on that basis.
I’m arguing to the Court, on the basis of these challenges, they appear to be pre-textual. And you can put aside that issue with [Ms. Franklin]. She doesn’t have anything about her that would cause the government any pause of having her as a juror, other than her race. She already served on a jury. Her answers were forthright, she had no problems of any kind. She didn’t respond, to any of the questions that the Court *318asked, in terms of any problems any jurors may have.
Id. at 141. In response, the government cited two distinctions between Franklin and Leureux: (1) that Ms. Franklin’s son was in prison, while Ms. Leureux’s son had been sentenced to probation, and (2) (somewhat counter-intuitively) that Ms. Leureux had stated that she was more reluctant to vote for a conviction.
As to this second distinction, Ms. Franklin had said that her son’s experience with the criminal justice system probably saved his life and “wouldn’t affect” her as a juror, while Ms. Leureux had said she was “a little nervous about [ ] the possibility of sending someone else’s son behind bars.” Id. at 145. Thus, though both jurors affirmed their ability to convict, the government kept a juror who admitted possible bias while striking a juror who claimed to be willing to put her son’s case out of mind. The government reasoned:
[T]he woman whose son had had a problem with the law for which he had gotten probation ... acknowledged that emotions of that type would — could come to bear when she deliberated, was deliberating about sons who were on trial, as these defendants are.
And my judgment, gut judgment, was that one juror [Leureux] was being more candid about their emotions and how they would play into the case, and one was not [Franklin], And one had a much different situation, where the son is actually incarcerated now, similar to the ones these defendants] are on trial for.
Id.
Without saying whether he credited the government’s expressed reasons for the strike, the magistrate judge denied defendants’ Batson motion on the ground that “[t]he record speaks for itself.” Id. at 141. We remanded because we were unable to resolve the Batson issue without a finding by the magistrate judge as to the credibility of the government’s race-neutral explanations. In Thomas I, we explained that:
[the] circumstances [] surely called for a credibility finding: Support for the notion that there was purposeful discrimination in the peremptory challenge may lie in the similarity between the characteristics of jurors struck and jurors accepted. Where the principal difference between them is race, the credibility of the prosecutor’s explanation is much weakened.
Thomas I, 303 F.3d at 145 (emphasis added, internal quotation marks omitted) (quoting Jordan v. Lefevre, 206 F.3d 196, 201 (2d Cir.2000)); see also Barnes, 202 F.3d at 156 (“The third-stage analysis thus compels courts to determine the credibility of the proffered explanations.”) (internal quotation marks omitted).
On remand, the magistrate judge took steps to comply with our instruction, observing (understandably) that the passage of nearly three years made its task more difficult:
[notwithstanding th[e] time lag, while I recognize the limitation that attends the reconstruction of credibility findings made three years ago, I have carefully read the transcript of the jury selection and find that the transcript of jury selection has sufficiently refreshed my recollection of the events in issue so that I can meaningfully comply with the [Thomas I ] panel’s instruction.
United States v. Thomas (“Supplemental Findings”), 98 CR 860(ERK), at 1-2 (E.D.N.Y. Oct. 3, 2002). The resulting findings, however, reflect a reliance on the transcript that is not substantially informed by any refreshed recollection, and consist in the main of findings that we held to be insufficient in Thomas I:
*319The Government justified its differential treatment of Ms. Leureux [and Ms. Franklin] on the basis of a distinction between an imprisoned son and a probated son, and it appears that I found that distinction non-pretextual when I observed that “the record speaks for itself[.]”
Id. at 3 (emphasis added, internal citations omitted). The magistrate judge upon remand thus made no new explicit finding with regard to the credibility of the government’s proffered explanations, pointing only to an apparent finding based upon a statement that “[t]he record speaks for itself.” Id. In light of our holding in Thomas I that a further credibility finding was required under the circumstances, 303 F.3d at 145, this is not enough.
Ill
As to the government’s peremptory strike of Ms. Campbell, the prosecutor responded to defendants’ Batson motion as follows:
I thought the tone that [Ms. Campbell] took when she was answering many of the Court’s questions evinced a flippancy, almost a kind of casual disregard for the proceedings.
Thomas I, 303 F.3d at 141.
Defense counsel denounced this explanation as pretextual. In ruling on the government’s flippancy explanation, the magistrate judge could not “say if that is true or not,” id. at 141, adding:
[Ms. Campbell] is not unique, she is one of several jurors, but she also was one of the people who forgot [to mention during general examination her] prior jury service.
IcL The magistrate judge’s Batson ruling as to Ms. Campbell cited the government’s waiver of opportunities to strike other black jurors,1 and relied on the absence of any apparent pattern of discriminatory strikes:
[A]t the time the government exercised both of their waivers, there were three African-Americans at that time who were not challenged. In other words, I don’t see a pattern any more than I[] see a pattern of challenging Hispanics.... Nor do I see a pattern in challenging only whites and Hispanics.
Id.
We found the magistrate judge’s findings with respect to Ms. Campbell insufficient in Thomas I, and remanded:
We have repeatedly emphasized that a trial court may not deny a Batson motion without determining whether it credits the race-neutral explanations for the challenged peremptory strikes[, since t]he credibility of an attorney offering a race-neutral explanation is at the very heart of [the Batson ] analysis.
Thomas I, 303 F.3d at 144 (internal citations and quotation marks omitted).
On remand, the magistrate judge acknowledged that
there was no specific finding on my part regarding Ms. Campbell[.] I did not find that her demeanor was or was not as described by the Government and / did not restore her to the panel on the basis of my observations that the Government did not engage in a pattern of deliberate exclusion of black jurors as evidenced by their waiver of challenges which left blacks on the jury. Accordingly if the Government actively sought *320 to exclude minority jurors, they would not have left three blacks on the panel.
Supplemental Findings at 3-4 (emphasis added, internal footnote omitted). This passage, like the original finding, explains and justifies reliance on the lack of any apparent pattern of racially-motivated strikes, but it does not amount to a credibility finding as to the prosecution’s proffered explanation for striking Campbell. This is insufficient to sustain the strike: “[t]he finding of an absence of pattern strikes is useful, but the wrongful strike of Ms. Campbell alone would implicate Bat-son.” Thomas I, 303 F.3d at 146; see also Batson, 476 U.S. at 97, 106 S.Ct. 1712 (“a ‘pattern’ of strikes against black jurors included in the particular venire might give rise to an inference of discrimination,” but that “examplef]” of an equal protection violation is “merely illustrative”).
IV
Under Batson’s burden-shifting procedure, the burden of production may shift to the non-movant, but the “ultimate burden of persuasion regarding racial motivation rests with, and never shifts from, the opponent of the strike.” Purkett v. Elem, 514 U.S. 765, 768, 115 S.Ct. 1769, 131 L.Ed.2d 834 (1995) (per curiam). The government thus is not required, when challenged, to persuade the court that its race-neutral reasons for striking jurors are valid or tactically sound; it is enough that they are the government’s reasons. But a finding to that effect is needed, and it is error to deny a Batson motion without determining whether' the prosecution’s race-neutral explanations for the challenged peremptory strikes are credible. Thomas I, 303 F.3d at 144; Barnes v. Anderson, 202 F.3d 150, 156 (2d Cir.1999). One way to do that is for the court to confirm the accuracy of the prosecutor’s explanation (e.g., that the juror was impatient or evasive); another is to find that the prosecutor’s stated reason for the challenge reflects the prosecutor’s good faith belief, even if the judge would not have stricken the same juror, or would have stricken the juror for another reason.
Here, the magistrate judge was unable to make any findings as to the credibility of the government’s stated reasons for challenging jurors Franklin or Campbell. This case thus seems to fall into the category of those in which the passage of time renders unavailable the findings that are mandated. The passage of time that explains the inability to make findings, however, does not obviate them. Because defendants were convicted by a jury that was not selected according to the Constitution, we must remand for a new trial. See Barnes, 202 F.3d at 157 (remanding to the district court for a new trial because further proceedings could not “shed reliable light upon the voir dire”); see also Patton v. Mississippi, 332 U.S. 463, 469, 68 S.Ct. 184, 92 L.Ed. 76 (1947) (“fO]ur holding does not mean that a guilty defendant must go free. For indictments can be returned and convictions can be obtained by juries selected as the Constitution commands.”).
CONCLUSION
For the foregoing reasons, defendants’ convictions are vacated and this matter is remanded to the district court for a new trial.