#### UNITED STATES, Appellee, v. David K. MENSAH, a/k/a Willberforce Appiah, Defendant, Appellant.

No. 12-1066.

United States Court of Appeals, First Circuit.

Dec. 16, 2013.

*791Judith H. Mizner, with whom Rheba Rutkowski, Assistant Federal Public Defender, and Miriam Conrad, Federal Public Defender, were on brief, for appellant.

Kelly Begg Lawrence, Assistant U.S. Attorney, with whom Carmen M. Ortiz, United States Attorney, was on brief, for appellee.

Before TORRUELLA, SELYA, and LIPEZ, Circuit Judges.

LIPEZ, Circuit Judge.

Appellant David Mensah successfully negotiated the complexities of United States immigration law twice: first, to be*792come a naturalized citizen under his own name and, second, to obtain a diversity visa under the false name Willberforce Ap-piah. His success, however, was short-lived. The government detected Mensah’s double dipping, and he was subsequently found guilty by a jury on a charge of unlawful procurement of naturalization, in violation of 18 U.S.C. § 1425(a), based on his concealment of his Appiah identity. On appeal, Mensah raises a host of errors, ranging from constitutional claims to the allegedly improper admission of propensity evidence. His most substantial claim is that the selection of his jury involved purposeful discrimination. *See Batson v. Kentucky,*476 U.S. 79, 86, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986). Although the issue is close, we conclude that the district court did not clearly err in allowing the prosecutor’s peremptory challenges to two Asian-American potential jurors. Hence, we affirm.

I.

The facts, as supported by the record, are as follows. Appellant Mensah entered the United States from Ghana in the early 1990s and received permanent legal resident status in 1995 pursuant to a diversity visa.1 Mensah obtained a Massachusetts driver’s license two years later. In October 2000, he applied for a diversity visa in the name of Willberforce Appiah,2 and a few months later, in February 2001, he applied for citizenship under his own name. In the naturalization application, Mensah responded “N/A” to a request for “[o]ther names used since you first became a permanent resident.” The application also asked whether Mensah had ever “knowingly committed any crime for which [he had] not been arrested.” Mensah checked the box labeled “No.” He also signed an affirmation on the form stating that “this application, and the evidence submitted with it, is all true and correct.”

In June 2001, Mensah followed up on the Appiah visa application by submitting a form titled “Supplemental Registration for the Diversity Visa Program.” He listed the same address in Ghana that he had used in the original Appiah application, again noting that mail should be sent there “c/o D.K. Mensah.” In December 2001, Mensah filed his final Appiah application for a diversity visa, along with an affidavit in his own name sponsoring Appiah for the visa. The government issued a diversity visa to Appiah in August 2002, and Mensah used it when he returned to the United States a few weeks later after a trip to Ghana.3 Shortly thereafter, he obtained a Massachusetts state identification card in Appiah’s name and, in May 2003, a driver’s license.

Meanwhile, in August 2001, Mensah was interviewed by the Immigration and Naturalization Service (“INS”) in connection with his naturalization application. After *793placing Mensah under oath, the examiner, Alton Saucier, asked him a series of questions, including whether Mensah had ever knowingly committed a crime for which he had not been arrested. Mensah responded that he had “never” done so. At the end of the interview, Mensah signed the application, swearing that it was “true to the best of my knowledge and belief.” Saucier recommended approval of Mensah’s naturalization application, and he became a citizen in September 2001 — in the midst of his activities to create a second identity as Willberforce Appiah.

In October 2006, the Massachusetts State Police (“MSP”) learned that Mensah had obtained driver’s licenses under both names, in violation of state law barring the use of false information to procure a license. *See*Mass. Gen. Laws ch. 90, § 24B. Officers obtained a warrant charging him-with violating section 24B and, a month later, arrested him in his car a few blocks from his home. During an inventory search of the vehicle, the officers found multiple documents bearing the false Appi-ah name. In January 2009, Mensah admitted in state court that sufficient facts existed to sustain a conviction under section 24B, and the case was continued without a finding.4

A subsequent investigation by Immigration and Customs Enforcement (“ICE”) led to Mensah’s indictment in this case in March 2010 on one count of unlawful procurement of naturalization, in violation of 18 U.S.C. § 1425(a).5 The government charged that Mensah had unlawfully obtained naturalization by making material false statements under oath during his naturalization proceedings, in violation of § 1015(a) — i.e., he allegedly procured naturalization, “contrary to law,” by making unlawful false statements in his naturalization application and interview.6 A Bill of Particulars filed by the government at Mensah’s request pointed to three false statements: (1) his response “N/A” on the naturalization application form, when asked if he had used other names since becoming a permanent resident, (2) his answer of “no” (by checking a box on the form), when asked if he had “ever knowingly committed any crime” for which he had not been arrested, and (8) his oral statement to INS Officer Saucier in August 2001 repeating that he had never knowingly committed such a crime.

Mensah moved to suppress the documents found in his car on the ground that the officers who arrested him unlawfully seized and searched the vehicle. The district court denied the motion. Characterizing the inspection of Mensah’s car as a warrantless inventory search, the court held that it was permissible under the Fourth Amendment because the officers had acted pursuant to “standardized policies.” *See*Section II *infra.*The district court also rejected Mensah’s *Batson*challenge to the government’s peremptory strikes of the only two Asian-Americans in the jury pool, crediting the prosecutor’s *794race-neutral reasons for excluding them. *See*Section III *infra.*

At trial, the government’s theory was that all three of the statements alleged to be false were untrue because, at the time they were made, Mensah had previously applied for the diversity visa using the fake Appiah name — a crime under 18 U.S.C. § 1001(a)(2).7 Thus, he knowingly lied in his naturalization application — in violation of 18 U.S.C. § 1015(a) — when he denied that he had used other names (by responding that the question was not applicable to him) and when he twice reported (once in the application and once in the interview) that he had never knowingly committed a crime for which he had not been arrested (the section 1001(a)(2) violation). The section 1015 violation then became the predicate for the section 1425(a) violation, i.e., he allegedly procured naturalization contrary to law by means of those unlawful false statements.8

Mensah did not dispute the facts underlying the unlawful procurement charge. He admitted that he had applied for a visa in the name of Willberforce Appiah and that he had answered the questions in the manner reported above while obtaining citizenship in his own name. His defense, instead, was that the government had failed to prove multiple elements of the crime beyond a reasonable doubt. Specifically, he argued that the government failed to show that (1) he *knowingly*committed a crime by submitting the Appiah diversity visa application, (2) the statements on the naturalization form were made under oath, (3) “N/A” as a response to the question about other identities was a false statement, and (4) he knew that he was statutorily ineligible for citizenship at the time that he applied for and obtained naturalization. The jury was not persuaded, finding Mensah guilty after two hours of deliberation.

On appeal, Mensah renews his Fourth Amendment challenge to the search and seizure of his vehicle and his *Batson*challenge to the prosecutor’s peremptory strikes of “the only Asian members of the jury venire.” He additionally claims that the evidence was insufficient to support the jury verdict, asserts error in certain jury instructions, and argues that the district court abused its discretion in allowing the government to introduce evidence concerning his driver’s license arrest.

II.

Mensah claims that the district court erroneously denied his motion to suppress the documents bearing the name Willber-force Appiah that were seized from his car after his arrest in November 2006, as well as unspecified statements concerning those documents that he made to officers. The documents were found on the front passenger floor and in the unlocked glove compartment during a search of his car that took place after Mensah was handcuffed and placed in a police cruiser. Among the items found with the Appiah name were a checkbook, a credit union membership card, and an insurance bill and receipt relating to two vehicles. The district court held that the troopers’ search of the car was permissible under the Fourth Amendment because the officers had followed *795standard MSP procedures for towing a vehicle and conducting an inventory search.

We review the district court’s ultimate ruling on suppression de novo, accepting its underlying factual findings unless clearly erroneous. *United States v. Wurie,*728 F.3d 1, 2-3 (1st Cir.2013). Because the court found a lawful inventory search, it did not address the government’s argument that the officers’ examination of the vehicle also was justified as a search incident to arrest. Without suggesting any reservations about the district court’s analysis, we choose to focus on the search-incident-to-arrest doctrine because it easily disposes of the claim of error. *See United States v. Sanchez,*612 F.3d 1, 4 (1st Cir. 2010) (noting that a district court order denying suppression may be affirmed on any ground supported by the record).

A warrantless search incident to arrest is permissible “when it is reasonable to believe that evidence of the offense of arrest might be found in the vehicle.” *Arizona v. Gant,*556 U.S. 332, 335, 343, 129 S.Ct. 1710, 173 L.Ed.2d 485 (2009). Here, the officers’ investigation had revealed that Mensah had obtained driver’s licenses under two different names, one of which was false. The troopers had a valid arrest warrant charging him with unlawfully obtaining a driver’s license under a false name. When Mensah was stopped while driving, he gave officers a license and registration in his own name. The dispositive issue is thus whether the officers could have reasonably believed that the license bearing Mensah’s second, false identity — or other documents showing that Mensah had secured a license under the Appiah name — also would be in the vehicle.

Mensah asserts that the government has offered, no facts to support an objectively reasonable belief that such evidence would be found in the car. As the government observes, however, the passenger compartment of a car is “by custom and necessity[] a common repository for motor vehicle-related documents.” Given that the officers knew that Mensah was using licenses in two different names, it would be reasonable for them to presume that he had obtained multiple licenses so that he could represent himself as a different person at his convenience. It would thus be reasonable for the officers to believe that he would have both licenses readily available in his vehicle.

Moreover, contrary to Mensah’s suggestion, it is irrelevant that the trooper conducting the search had in mind MSP policy governing towing and inventory searches rather than the Supreme Court’s precedent on searches of vehicles incident to arrest. *See Florida v. Jardines,*— U.S. -, 133 S.Ct. 1409, 1416, 185 L.Ed.2d 495 (2013) (“[A] stop or search that is objectively reasonable is not vitiated by the fact that the officer’s real reason for making the stop or search has nothing to do with the validating reason.” (emphasis deleted)); *United States v. Hadfield,*918 F.2d 987, 993 (1st Cir.1990) (“[A]n officer’s state of mind or subjective intent in conducting a search is inapposite as long as the circumstances, viewed objectively, justify the action taken.”). Hence, “the likelihood of discovering offense-related evidence authorized the search in this case.” *Gant,*556 U.S. at 344, 129 S.Ct. 1710.

The district court thus correctly denied Mensah’s motion to'suppress.

III.

Mensah claims that the prosecutor exercised his peremptory challenges to exclude two Asian-Amerieans from the jury solely on accpunt of their race, in violation of the Equal Protection Clause.

*796A. Legal Background

In *Batson v. Kentucky,*the Supreme Court reaffirmed the longstanding principle that a criminal defendant’s equal protection rights are violated when jury selection at his trial is “affected by invidious racial discrimination.” *United States v. Girouard,*521 F.3d 110, 112 (1st Cir. 2008); *see also Miller-El v. Dretke,*545 U.S. 231, 238, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005); *Batson,*476 U.S. at 85-87, 106 S.Ct. 1712. The obstacle to eradicating such impermissible motivation has been “the practical difficulty of ferreting out discrimination in selections discretionary by nature, and choices subject to myriad legitimate influences, whatever the race of the individuals on the panel from which jurors are selected.” *Dretke,*545 U.S. at 238, 125 S.Ct. 2317. Because peremptory strikes have long been used to exclude minorities from juries, the Court in *Batson*outlined a three-part burden-shifting framework — now commonly'called a *“Bat-son*challenge” — under which a defendant can dispute a prosecutor’s use of peremptory strikes against minority jurors and show an equal protection violation:

> First, a defendant must make a prima facie showing that a peremptory challenge has been exercised on the basis of race. Second, if that showing has been made, the prosecution must offer a race-neutral basis for striking the juror in question. Third, in light of the parties’ submissions, the trial court must determine whether the defendant has shown purposeful discrimination.

*Miller-El v. Cockrell,*537 U.S. 322, 328-29, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) (citing *Batson,*476 U.S. at 96-98, 106 S.Ct. 1712) (specific citations omitted).9

The parties here do not dispute that Mensah has made a satisfactory prima fa-cie showing and that the government has proffered race-neutral reasons for its strikes. We therefore focus exclusively on the third step: was the district court correct that Mensah failed to carry his burden of demonstrating purposeful discrimination? *See United States v. Lara,*181 F.3d 183, 194 (1st Cir.1999) (noting that “we can truncate the usual inquiry” where a preliminary step is undisputed).

The party opposing a peremptory strike bears the burden of proof throughout the inquiry. *Girouard,*521 F.3d at 113. We review for clear error the district court’s factual determination that the prosecutor was not motivated by race, *United States v. Charlton,*600 F.3d 43, 50 (1st Cir.2010), mindful that “determinations of credibility and demeanor lie peculiarly within a trial judge’s province,” *Snyder v. Louisiana,*552 U.S. 472, 477, 128 S.Ct. 1203, 170 L.Ed.2d 175 (2008) (internal quotation marks omitted). The Supreme Court has noted the importance of “the trial court’s first-hand observations” because “ ‘the best evidence [of discriminatory intent] often will be the demeanor of the attorney who exercises the challenge,’ ” along with “whether the juror’s demeanor can credibly be said to have exhibited the basis for the strike attributed to the juror by the prosecutor.” *Id.*(quoting *Hernandez v. New York,*500 U.S. 352, 365, 111 S.Ct. 1859, 114 L.Ed.2d 395 (1991)) (alteration in original). A factual error by the district court is “clear” only where “we are left with the definite and *797firm conviction that a mistake has been committed.” *United States v. Gonzalez-Melendez,*594 F.3d 28, 35 (1st Cir.2010) (internal quotation mark omitted).

In evaluating a claim of purposeful discrimination under *Batson,*“a court must undertake a sensitive inquiry into such circumstantial and direct evidence of intent as may be available,” 476 U.S. at 93, 106 S.Ct. 1712 (internal quotation mark omitted), considering “all relevant circumstances,” *id.*at 96, 106 S.Ct. 1712; *see also Dretke,*545 U.S. at 251-52, 125 S.Ct. 2317 (stating that the court must “assess the plausibility of th[e prosecutor’s] reason in light of all evidence with a bearing on it”); *Hernandez,*500 U.S. at 363, 111 S.Ct. 1859 (“[A]n invidious discriminatory purpose may often be inferred from the totality of the relevant facts.... ” (alteration in original) (internal quotation mark omitted)). In keeping with the totality-of-the-circumstances approach, the analysis may take into account whether explanations for challenges made later in the process shed light on an earlier strike. *See Snyder,*552 U.S. at 478, 128 S.Ct. 1203 (stating that, “if there were persisting doubts as to the outcome” in one instance, “a court would be required to consider the strike of [another individual] for the bearing it might have” on the other challenge); *see also Charlton,*600 F.3d at 55 (Lynch, C.J., concurring) (noting that seemingly permissible individual strikes may need “a second look” if, when taken together, they “create a concern that certain groups are underrepresented”).

Courts frequently look to “numeric” evidence to detect impermissible discrimination, including “the percentage of a particular group removed from the venire by the challenged strikes” and “the percentage of strikes directed against members of a particular group.” *Aspen v. Bissonnette,*480 F.3d 571, 577 (1st Cir.2007). Comparing the treatment of white and non-white potential venire members also may shed light on the prosecutor’s intentions. “If a prosecutor’s proffered reason for striking a black panelist applies just as well to an otherwise-similar nonblack who is permitted to serve, that is evidence tending to prove purposeful discrimination to be considered at *Batson’s*third step.” *Dretke,*545 U.S. at 241, 125 S.Ct. 2317; *see also Charlton,*600 F.3d at 50-51 (noting that circumstances bearing on racial animosity include “ ‘whether similarly situated jurors from outside the allegedly targeted group were permitted to serve’ ” (quoting *Aspen,*480 F.3d at 577)).

The circumstances here differ from the classic *Batson*ease, in which a prosecutor exercises peremptory strikes against jurors who are of the same nonwhite race as the defendant. In this case, Mensah, who is black, contests the prosecutor’s challenges of two Asian-American jurors. Hence, Mensah cannot argue that the prosecutor’s strikes were impermissibly based on an assumption that the struck jurors would favor him because they were of the same race. *See Batson,*476 U.S. at 97, 106 S.Ct. 1712 (stating that “the prosecutor may not rebut the defendant’s prima facie case of discrimination by stating merely that he challenged jurors of the defendant’s race on the assumption — or his intuitive judgment — that they would be partial to the defendant because of their shared race”). The Supreme Court has long recognized, however, that whatever the defendant’s race, he has “the right to be tried by a jury whose members are selected by riondiscriminatory criteria.” *Powers v. Ohio,*499 U.S. 400, 404, 111 S.Ct. 1364, 113 L.Ed.2d 411 (1991) (holding that a white defendant may challenge the exclusion of blacks from his jury). Accordingly, it is equally impermissible for the prosecutor to use race as a proxy for *798some other trait that he believes would make -non-white jurors less likely than a white juror to convict the defendant. *See id.*at 416, 111 S.Ct. 1364 (“[R]ace prejudice stems from various causes and may manifest itself in different forms.”).

To sum up, “the Equal Protection Clause forbids the prosecutor to challenge potential jurors solely on account of their race,” whatever the justification. *Batson,*476 U.S. at 89, 106 S.Ct. 1712. Faced with a claim that such targeting occurred, we must carefully examine all of the pertinent facts, giving due deference to the district court, to determine “whether the defendant ha[s] met his burden of proving purposeful discrimination on the part of the State.” *Id.*at 90, 106 S.Ct. 1712.

B. The Voir Dire

Jury selection in this case consisted of a three-part process of examining potential jurors’ backgrounds, followed by four rounds of peremptory challenges. Initially, the district court asked a pool of about fifty potential jurors two dozen questions to ascertain the individuals’ suitability for the jury. These inquiries included whether the venire members had family or close friends employed in law enforcement, involved in. an immigration proceeding, or charged with a criminal offense, as well as whether any scheduling issues would interfere with their service on the jury. The potential jurors raised their hands to show an affirmative answer as each question was asked. In the next step of the process, fourteen of those individuals were randomly chosen to sit in the jury box, and each potential juror who had signaled a positive response to any of the preliminary questions was called to sidebar for inquiry about his or her responses. When the sidebar interview resulted in jurors being dismissed for cause, the jury box was refilled and the sidebar process repeated.

Once fourteen jurors cleared the sidebar questioning, the district court moved to step three: asking each of the jurors for their occupations and, if married, their spouses’ occupations. The first round of peremptory challenges then took place. In round one, the prosecutor successfully struck three jurors: one whose mother had been deported in 2005, another whose girlfriend currently was in amnesty proceedings, and a lawyer whose practice consisted primarily of criminal defense work. The prosecutor’s attempt to strike a fourth person, Deirdre Pritchett, drew a *Batson*challenge from defense counsel because Pritchett was “the only African-American person in the jury.” When the prosecutor attributed the challenge to Pritchett’s “relatives who were involved with criminal offenses,” defense counsel pointed out that Pritchett was not close with those family members and that a white juror whom the government did not strike had a friend who had been in jail. She criticized the justification as a pretext for a race-based motive. The district court told the prosecutor that it was “inclined to agree” with Mensah’s counsel: “I don’t see that your reasons stated are sufficient to overcome the fact that she apparently is the only person of color in the whole venire.”

The government then withdrew its strike “in an abundance of caution,” and Ms. Pritchett was seated. The prosecutor, however, immediately moved to exclude an Asian-Ameriean potential juror named Yuqing Zhang. The defense again objected on *Batson*grounds, arguing that the government was attempting to exclude Zhang from the jury based on his race. The government proffered that it sought to exclude Zhang because he was a professor at Boston University Medical School with an expertise in biology and might be “too scientific” in his application of the reasonable doubt standard. The district *799court overruled the defense’s objection, and Zhang became the government’s final strike during the first round. • The defense also exercised four peremptory challenges during that round.10

After the court clerk re-filled the seats vacated by the struck jurors and the sidebar discussions and occupation inquiries were completed, the second round of peremptory challenges began with defense counsel striking a potential juror who was a police cadet. The government followed by striking a young, single woman named Kimberly Faria, and the defense then struck another young, single woman named Mary Conway. The jury box was again re-filled by adding three individuals, including an Asian-American woman named Quyen Diep. The sidebar and occupation inquiries followed, leading into the third round of peremptory challenges.

The government had the first option to challenge in this round, but passed. The defense then struck two individuals and, given another opportunity, the government challenged Diep, a young, single accountant. The defense again objected on *Bat-son*grounds, noting that “[t]his is the second Asian juror who’s been seated and the second Asian juror who[m] [the prosecutor] has struck.” Protesting that the challenge had nothing to do with race, the prosecutor noted that Diep was single and young. The defense decried the rationale as pretextual, asserting that there were “plenty” of single and young people on the jury and noting that the prosecutor had now sought to exclude both the only African-American and both Asians. The prosecutor declined the court’s invitation to say more. The judge took a few minutes to consider the matter and, after resuming the proceedings, asked the prosecutor to restate his grounds for striking Diep. The prosecutor responded: “She does appear to be young to me, a young person, and she’s a young, single person. I question her life experience based on that Judge.” Defense counsel then reiterated that she believed the jury already included “quite a number of single people.” She pointed specifically to Conway, although Conway had not in fact been seated on the jury because she was struck by the defendant.

The court allowed the challenge of Diep “on the stated grounds of the government.” The jury box again was refilled, the preliminaries were performed, and counsel were offered a fourth round of peremptory challenges. None was exercised. During the ensuing discussion about various trial matters, defense counsel noted for the record, in further response to the government’s strike of Diep, that the government had not objected to a white male juror named Conley, the last individual seated, who also was young and single. The court, in subsequently announcing that Conley would be one of the two alternates (because he was the last juror called), noted in an aside that Conley was not yet in the jury box when Diep was challenged.

The court returned to the *Batson*issue at the start of the next day’s proceedings:

> [J]ust for the record, with respect to the impanelment and the *Batson*challenge that was made by the defendant with respect to the admission of the potential juror, Miss Diep, during voir dire this Court overruled defense counsel’s *Bat-son*objection to the prosecutor’s use of a peremptory challenge to strike Miss Diep ... on the alleged basis of her race. The prosecutor offered a race-neutral explanation for striking Miss Diep that she was young and single and, *800as a result, had limited life experience. At the time the peremptory strike was exercised, Miss Diep was the only potential juror seated in the jury box who both appeared to be young and answered that she was single.

> In addition, the prosecution had previously used a peremptory challenge to strike Miss Kimberly Faria, ... who also appeared to be young and had answered that she was single. The Court considers the prosecution’s reasoning to be credible and sustains the peremptory challenge.

Although the court did not reopen the issue for further consideration, it allowed the attorneys to supplement the record. Defense counsel clarified that her objection was not solely to Diep’s exclusion, but to the challenge of both potential Asian jurors. She also reiterated that the government had allowed Conley to remain on the jury despite a professed objection to young, single jurors.

The prosecutor countered that Conley was not comparable to Diep because they had different jobs, and he noted that, when Conley was seated, the government was saving its last challenge “in an abundance of caution for somebody ... very undesirable.” Defense counsel questioned the reliance on different professions, noting that Diep was an accountant and Conley a financial analyst. The court made no further rulings and moved on to other matters. The jury thus consisted of one African-American juror and eleven white jurors.

C. Discussion

The forgoing recitation of facts well illustrates “the practical difficulty” of distinguishing between impermissible discrimination in jury selection and the prosecutor’s legitimate exclusion of jurors based on their personal characteristics and background. *Dretke,*545 U.S. at 238, 125 S.Ct. 2317. As we shall explain, both views of the prosecutor’s choices are plausible here. In the end, however, it is the very closeness of the question that determines the outcome of our inquiry.

1. Indications of Discrimination

The numeric evidence in this case is particularly strong in suggesting that race was a motivating factor in the government’s exercise of its peremptory challenges. The prosecutor struck, or attempted to strike, all of the non-white members of the venire. Both Asian-Americans were excluded from the jury, and the prosecutor was pressured by the court to withdraw the strike of Deirdre Pritchett — the only African-American. The prosecutor also struck the only obviously Hispanic individual, Carlos Alves, the juror whose mother had been deported in 2005.

In addition, the prosecutor’s rationale for striking Diep — that she was young and single — was flimsy in two respects. First, the prosecutor failed to explain why age and marital status were pertinent factors here. *See Batson,*476 U.S. at 98, 106 S.Ct. 1712 (“The prosecutor ... must articulate a neutral explanation *related to the particular case to be tried.”*(emphasis added)). Even after defense counsel complained that the strike appeared pretextual because there were “plenty” of single and young people on the jury, the prosecutor declined the district court’s offer to elaborate on his reasoning. When the prosecutor subsequently restated his grounds for the strike at the court’s request, the prosecutor added that he “question[ed] her life experience based on that.” Again, however, he drew no connection between limited life experience and the crime. Although courts have accepted youth and unmarried status as legitimate reasons for striking *801jurors, *see, e.g., Rice v. Collins,*546 U.S. 333, 341, 126 S.Ct. 969, 163 L.Ed.2d 824 (2006) (“It is not unreasonable to believe the prosecutor remained worried that a young person with few ties to the community might be less willing than an older, more permanent resident to impose a lengthy sentence for possessing a small amount of a controlled substance.”); *United States v. Mack,*78 Fed.Appx. 171, 180 (3d Cir.2003) (stating that “peremptory challenges based on age and marital status in the context of narcotics cases are logical and legitimately race-neutral”), allowing such strikes in the absence of an articulated, plausible link to the crime at issue creates the potential for a readily available pretext for discrimination.

Second, the prosecutor chose not to exercise strikes against at least two potential jurors who, but for their race, appeared similarly situated to Diep. The prosecutor passed on both Conway, a young, single woman, and Conley, a young, single man with a profession similar to Diep’s (he was a financial advisor, she an accountant). As discussed above, the fact that a prosecutor’s proffered reason for striking a minority juror could have applied with equal weight to white jurors who were not struck may support an inference of racial discrimination. *See Snyder,*552 U.S. at 483-84, 128 S.Ct. 1203. Moreover, although the proffered rationale for striking Zhang — a concern about the way a scientist would evaluate reasonable doubt — is plausible, the subsequent strike of Diep continued the prosecutor’s pattern of challenging every non-white juror and thus places that justification in a different light. *See Charlton,*600 F.3d at *55*(Lynch, C.J., concurring) (recommending “a second look” in such circumstances).

Also, given that this case involves an immigration offense, we must be sensitive to the racial stereotypes that could be at play. For example, the fact- that- many Asian-Americans come from immigrant communities may lead to the unwarranted assumption that *all*Asian-Americans have undue sympathy for non-white individuals seeking to become United States citizens. While personal exposure to the immigration system may be an appropriate basis for a peremptory challenge, we must take care to maintain the line between such strikes and those that rely solely on racial or ethnic stereotypes.

2. The Non-Discriminatory Inferences

Despite our reservations, we must take into account “all relevant circumstances,” *Batson,*476 U.S. at 96, 106 S.Ct. 1712, and multiple factors give a different impression when examined in context. First, from a numeric perspective, although no Asian-Americans were left on the jury, there were only two such individuals in the veni-re. Hence, with the strike of Zhang unexceptionable on its own, the elimination of “all” Asian-Americans here is substantially different from a case in which the numbers are larger and a pattern is inescapably apparent in the prosecutor’s strikes. *See, e.g., Snyder, 552*U.S. at 476, 128 S.Ct. 1203 (prosecutor used peremptory strikes to eliminate all five black prospective jurors); *Dretke,*545 U.S. at 240-41, 125 S.Ct. 2317 (prosecutor used peremptory strikes for ten African-American members of the venire panel, 91 percent of those eligible); *Powers,*499 U.S. at 403, 111 S.Ct. 1364 (prosecutor used seven of ten peremptory challenges to strike black members of the jury panel); *Sims v. Brown,*425 F.3d 560, 573 (9th Cir.2005) (prosecutor used eight of first twelve peremptory challenges to strike four African-American and four Hispanic venire panelists, leaving no black jurors and one His*802panic-surnamed individual).11 To be sure, the prosecutor in this case also struck the one identifiably Hispanic juror, Alves, and attempted to strike the only African-American, Pritchett. But the Alves strike was plainly appropriate for the neutral reason that his mother had been deported, and the prosecutor both offered a facially neutral reason for Pritchett (her incarcerated family members) and did not persist. Thus, as is common, the numbers considered in isolation are inconclusive. *See generally Charlton,*600 F.3d at 52-53 (cautioning against reliance on “ ‘just numbers alone’” (quoting *Girouard,*521 F.3d at 116)); *id.*at 55 (Lynch, C.J., concurring) (noting that “objections based solely on numerical effects are inherently problematic”); *United States v. Bergodere,*40 F.3d 512, 516 (1st Cir.1994) (“A defendant who advances a *Batson*argument ordinarily should come forward with facts, not just numbers alone.” (internal quotation marks omitted)).

Second, the comparative evidence is similarly equivocal. Mensah argues that the prosecutor’s explanation that he challenged Diep because she is young and single is belied by the prosecutor’s failure to strike two other young, single individuals — Conway and Conley. In context, however, the demographic equivalence between those two jurors and Diep is less noteworthy. The prosecutor did bypass Conway when he had the opportunity to challenge her early in the second round. He instead exercised his first peremptory strike in that round against Kimberly Fa-ria, whom the district court described as another young, single woman. The very next strike, however, was by the defendant against Conway. That strike could fairly be described as predictable given the professions of Conway’s family members: an assistant district attorney (her father), a judge (her grandfather), attorneys (an aunt and uncle), and a police officer (another uncle). The prosecutor, therefore, had little opportunity — or incentive — to strike Conway before the defendant eliminated her.

Moreover, the strike of Faria appeared consistent with the prosecutor’s “young and single” rationale for striking Diep. Fa-ria, a teacher’s assistant, had answered none of the opening questions affirmatively and, hence, had no other revealed objectionable characteristics. Conley, meanwhile, was seated when the government had only one remaining strike.12 The prosecutor’s explanation that he was being cautious about exercising his final peremptory challenge, which would have meant seating a replacement juror whom the prosecutor would have no opportunity to strike, is on its face plausible. *See Dretke,*545 U.S. at 249-50, 125 S.Ct. 2317 (noting the prosecutors’ need “to exercise prudent restraint in using strikes” late in the jury-selection process). The prosecutor reasonably could have chosen to stick with a young, single financial analyst to avoid the risk of a juror who, for example, had a family member or close friend involved in immigration proceedings — as had two pri- or venire members whom the prosecutor had struck (Alves, described above, and *803Joseph Leary, whose girlfriend was in the process of “fighting for amnesty” from Honduras).13

3. The District Court’s Evaluation

Given the competing inferences that could be drawn from the prosecutor’s exercise of peremptory challenges, the district court’s on-the-scene assessment looms large. To its credit, the court took the *Batson*issue seriously and carefully considered the circumstances. It balked at the strike of Pritchett and likewise hesitated when defense counsel objected to the strike of Diep, halting the proceedings and then asking the prosecutor to restate his grounds for the strike. Before allowing the strike, the court probed defense counsel’s objection that other single young persons had been seated. It revisited its initial ruling the next day, making explicit its previous implicit finding that the prose^ cutor had genuinely relied on Diep’s age and marital status.

Although we commend the court’s diligence, it might ideally have gone a step further. The court did not explicitly respond to defense counsel’s repeated urging that the strikes of both Asian-Americans be evaluated together. That gap, in combination with the prosecutor’s failure to explain how the young-and-single rationale related in any way to the particulars of this case, leaves us with some lingering concern. *See United States v. Perez,*35 F.3d 632, 636 (1st Cir.1994) (urging trial judges not only to state whether they “find[] the proffered reason for a challenged strike to be facially race neutral or inherently discriminatory,” but also “why [they] choose[] to credit or discredit the given explanation”). Yet, this is not a case where “[t]he strikes correlate^] with no fact as well as they correlate with race.” *Dretke,*545 U.S. at 266, 125 S.Ct. 2317. Rather, the evidence permits competing plausible interpretations. *See Lara,*181 F.3d at 195. Given the defendant’s burden of persuasion, and the deference owed to the district court’s assessments of credibility and demeanor, we cannot conclude that the court clearly erred in finding that no improper discrimination occurred. *See Rice,*546 U.S. at 343, 126 S.Ct. 969 (Breyer, J., concurring) (observing that appellate courts “must[ ] grant the trial courts considerable leeway in applying *Batson”*because, “in a borderline case,” the trial judge is best situated to decide if “a prosecutor’s hesitation or contradiction reflect (a) deception, or (b) the difficulty of providing a rational reason for an instinctive decision”); *Lara,*181 F.3d at 195 (“[W]hen the evidence gives rise to competing interpretations, each plausible, the factfinder’s choice between them cannot be clearly erroneous.”).

We therefore affirm the district court’s rejection of appellant’s *Batson*challenge.

IV.

Mensah argues that the jury instructions given by the district court erroneously defined multiple essential elements of the crimes implicated in the charge that he violated 18 U.S.C. § 1425(a). Section 1425(a) itself makes it a crime to knowingly procure, “contrary to law, the naturalization of any person.” The indictment alleged that Mensah knowingly procured naturalization “contrary to law” because he had knowingly made false statements under oath in his application and interview, in violation of 18 U.S.C. § 1015(a). The identified false statements were that (1) he had never knowingly committed any crime for which he had not been arrested and (2) *804he had not used other names while he was a permanent resident, the latter assertion implied from his response “N/A” to the application question about other names.14 According to the government, the crime that Mensah falsely denied committing was knowingly making a false or fraudulent statement in a matter within the jurisdiction of the United States, in violation of 18 U.S.C. § 1001(a)(2). The underlying statement was the fraudulent visa application Mensah filed under the Appiah name.

Mensah and the government submitted numerous proposed jury instructions to the court to cover the elements of section 1425(a) in the context of this layered trio of crimes. Mensah asserts three errors in the court’s choices: (1) improperly refusing to give his requested instruction on when a statement may be deemed “false,” (2) erroneously defining “under oath,” and (3) giving an “unlawful procurement” instruction that impermissibly relieved the government of its burden of proof as to that element. We consider each of these in turn.

A. The False Statement Instruction

Focusing on his “N/A” response, Men-sah contends that the district court, by giving an inadequate explanation of when a statement may be found “false,” misstated the government’s burden to prove falsity. The court instructed the jury that “[a] statement is false if it was untrue when made.” Mensah asserts that the court should have given a much more elaborate description of falsity, telling the jurors, inter alia, that the government needed to prove that “what he *said*was false,” that “[i]t is insufficient for the government to prove that his statement implied something that was not true,” and that proof of a false statement requires “pro[of] beyond a reasonable doubt that the statement was false under any objectively reasonable interpretation of the question and answer.” Mensah also proposed an ambiguity instruction, which included the following: “Even an answer that is deliberately evasive or misleading is not false, unless it is false on its face. Nor is an unresponsive answer false. It is up to the person asking the question to clarify an ambiguous or evasive answer.”

A trial court’s rejection of proposed instructional language is reversible error “only in the ‘relatively rare case’ in which ‘the requested instruction was (1) substantively correct; (2) not substantially covered elsewhere in the charge; and (3) concerned a sufficiently important point that the failure to give it seriously impaired the defendant’s ability to present his or her defense.’ ” *United States v. Gonzalez,*570 F.3d 16, 21 (1st Cir.2009) (quoting *United States v. Prigmore,*243 F.3d 1, 17 (1st Cir.2001)). This is not such a case.

Mensah argues, in effect, that the district court should have advised the jury that his “N/A” reply could not be found false unless it was literally untrue, and that it was not enough to find that his response was misleading, evasive, unresponsive, or ambiguous. Such an instruction, however, would have been at least misleading, and arguably incorrect. Imprecision or incompleteness in an answer to a straightforward inquiry — such as the request for “other names used” — does not foreclose a finding of falsity. *See, e.g., United States v. Boskic,*545 F.3d 69, 87 (1st Cir.2008) (noting that a jury can properly find falsity based on incomplete answers). Mensah does not argue that the *question*he was asked about other names was ambiguous, and therefore his invoca*805tion of *United States v. Rowe,*144 F.3d 15 (1st Cir.1998), does not help him. *See id.*at 21 (“[I]n a false statement prosecution, an answer to a question is not fraudulent if there is an objectively reasonable interpretation of *the question*under which the answer is not even false.” (emphasis added)). In addition, Mensah has never claimed that “N/A” was a literally true statement that could not properly be found “false on its face.”15

Hence, instructing the jury on literal truth or falsity, ambiguity, or any similar linguistic defense would have run the risk of sending the jury off track. Indeed, the government’s argument could not have been more straightforward: because Men-sah had created a second identity as Appi-ah, he made a false statement when he wrote that the inquiry about other names was “not applicable.” On this record, then, the only pertinent focus of the jury’s deliberations — as the district court properly instructed — was to determine whether “N/A” was an “untrue [statement] when made.”

Moreover, the district court’s rejection of his proposed instruction did not prevent Mensah from presenting his theory of falsity to the jury. Specifically with respect to “N/A,” counsel argued that it could not be a false statement because his INS interviewer, Saucier, testified that he did not know what the abbreviation meant, and Saucier never asked Mensah to explain his response. In effect, counsel asked the jury to conclude that “N/A” for Mensah had no particular meaning — and could therefore not be deemed “false.” In this regard, counsel stated: “Now, ‘N/A’ sounds like something a lawyer might put down and' not have reviewed until after Mr. Mensah signed the application.” The jurors thus heard the gist of Mensah’s argument that he could not be found guilty unless “what he *said*was false.”

Accordingly, we find neither error in, nor harm from, the court’s refusal to give Mensah’s requested falsity instruction.

B. The Definition of “Under Oath”

Mensah asserts that the district court failed to properly instruct the jury on the element of section 1015(a) requiring that the prohibited false statement be made “under oath.”16 He maintains that a statement is made “under oath” only, if it is given after a *verbal*warning, from an authorized person, that falsity will be prosecuted as perjury. The district court rejected that narrow construction of the requirement, and instructed the jury as follows:

> A statement is made under oath if the defendant took an oath to testify truly before an agencyf ] authorized by law to administer oaths or if the defendant, under penalty of perjury, subscribed as true written information submitted to the agency.

Although Mensah acknowledges that the instruction as given followed accepted practice, see Leonard B. Sand, et al., 2-33 *Modern Federal Jury Instructions-Criminal*¶ 33.02 (Instruction 33-11), he claims *806that it improperly “ignore[d] the distinction between swearing an oath before a qualified official and endorsing a document under a written perjury warning.”

We disagree that the distinction between a sworn oath following a verbal warning and a written declaration expressly made subject to perjury matters here. Although making a statement “under oath” commonly is associated with a verbal swearing — such as that traditionally required of witnesses at a trial — federal law recognizes that oaths may be in writing and treats a written statement “subscribed ... as true under penalty of perjury” as equivalent to such a penned oath. 28 U.S.C. § 1746.17 Mensah cites no precedent holding that the oath element of section 1015(a) may be satisfied only with proof of a *verbal*warning or oath, and we see no rationale for excluding the oath requirement in that provision from the reach of section 1746.

Indeed, the generic legal definition of an “oath” makes no reference to a verbal act. *Black’s Law Dictionary*defines an oath as “[a] solemn declaration, accompanied by a swearing to God or a revered person or thing, that one’s statement is true or that one will be bound to a promise.” *Black’s Law Dictionary*1101 (8th ed.2004). Federal Rule' of Evidence 603, which states that a witness “must give an oath or affirmation to testify truthfully,”18 is similarly general. The Rule provides that the requisite declaration “must be in a form designed to impress that duty on the witness’s conscience” — but does not say that only a verbal warning or response suffices. Hence, it appears that the inquiry into whether an oath has been given is routinely treated as a question of substance rather than form: “[it] turns on whether the declarant expressed the fact that he or she is impressed with the solemnity and importance of his or her words and of the promise to be truthful, in moral, religious, or legal terms.” *United States v. Bueno-Vargas,*383 F.3d 1104, 1110 (9th Cir.2004).

Section 1746 thus reflects an accepted view of the “under oath” requirement in allowing a written statement made under penalty of perjury to substitute for a formal oath. *See Bueno-Vargas,*383 F.3d at 1111 (holding that “signing a statement under penalty of perjury satisfies the standard for an oath or affirmation”); 2 Wayne R. LaFave, *Search and Seizure*§ 4.3(e), at 659 (5th ed.2012) (noting that, to satisfy the Fourth Amendment’s “Oath or affirmation” clause, “the ‘true test’ is whether the procedures followed were such ‘that perjury could be charged there[o]n if any material allegation contained therein is false’ ”) (quoting *Simon v. State,*515 P.2d 1161, 1165 (Okla.Crim.App.1973)). Men-sah signed the following statement on his *807naturalization application: “I certify ... under penalty of perjury under the laws of the United States of America that this application, and the evidence submitted with it, is all true and correct.” Given section 1746 and the other legal authority described above, it is plain that the district court properly instructed the jury on the “oath” element of section 1015(a). *Cf. Bueno-Vargas,*383 F.3d at 1112 (“Because [the declarant] gave the Statement under penalty of perjury, [he] knew that he was making a solemn promise ... that all the information he was providing was true and correct.”).19

C. The Unlawful Procurement Instruction

The central element of Mensah’s crime of conviction, 18 U.S.C. § 1425(a), is the knowing “procure[ment], contrary to law,” of naturalization. Mensah’s proposed instruction on unlawful procurement was as follows:

> To establish this element [that defendant procured naturalization as a result of the false testimony] the government must prove that defendant obtained United States citizenship as a result of the misrepresentations alleged in the Indictment. This means that the government must prove that if the defendant had provided the immigration authorities with truthful evidence, the authorities would have determined that he was statutorily ineligible for citizenship.

The court instead gave the following instruction:

> [T]he government must prove that if the defendant had provided the Immigration authorities with truthful information it would have raised a fair inference that defendant was not eligible for naturalization.

Mensah argues that the court’s instruction was flawed because the jurors should have been told that they needed to find a “but for” connection between any misrepresentations and the grant of citizenship— and not merely that it would be “fair to infer” such a connection. He asserts that the court’s instruction improperly shifted the burden of proof by including an evi-dentiary presumption in favor of the government, allowing conviction without a showing that he had in fact procured naturalization “contrary to law.” Mensah argues that the government needed to prove beyond a reasonable doubt (1) that he was ineligible for citizenship, (2) how he was ineligible, and (3) the alleged misrepresentations that obscured this ineligibility.

In rejecting Mensah’s instruction, the district court relied on *Kungys v. United States,*485 U.S. 759, 108 S.Ct. 1537, 99 L.Ed.2d 839 (1988), a fractured decision in which the Supreme Court considered, inter alia, when a misrepresentation is “material” in the context of naturalization challenges and when such a misrepresentation “procured” a naturalization certificate within the meaning of the statute.20 The *808Court majority concluded that the materiality inquiry was “whether the misrepresentation or concealment ... had a natural tendency to affect[ ] the official decision.” *Id.*at 771, 108 S.Ct. 1537; *see also id.*at 772, 108 S.Ct. 1537 (describing the inquiry as “whether [the concealments or misrepresentations] had a natural tendency to influence the decisions of the Immigration and Naturalization Service”).

The more complex part of *Kungys*was the discussion on what must be proved, in addition to materiality, to establish that citizenship was “procured” through misrepresentations. The Seventh Circuit has summarized well the Court’s splintered response to that inquiry:

> The *Kungys*majority held that there are “four independent requirements” to the offense of procuring citizenship by misrepresentation: “the naturalized citizen must have misrepresented or concealed some fact, the misrepresentation or concealment must have been willful, the fact must have been material, and the naturalized citizen must have procured citizenship as a result of the misrepresentation of concealment.” *Kungys,*485 U.S. at 767, 108 S.Ct. 1537. So a majority of the Justices agreed that “materiality” and “procurement” are separate elements, and satisfaction of one does not necessarily mean satisfaction of the other. A majority also agreed that, at a minimum, the procurement requirement “demands ... that citizenship be obtained as a result of the application process in which the misrepresentations or concealments were made.” *Id.*at 776, 108 S.Ct. 1537. The Court split, however, over what else procurement means. Justice Stevens, speaking for two others, advocated what amounts to a “but for” test — that the government has to establish that citizenship would not have been conferred but for the misrepresentation. Justice Sca-lia, joined by two others, rejected this construction because it would make the materiality requirement meaningless, “requiring, in addition to distortion of the decision [ (procurement) ], a natural tendency to distort the decision [ (materiality)].” *Id.*But Justice Scalia and company did agree that procurement requires more than just obtaining citizenship “as a result of the application process in which the misrepresentation or concealments were made.” To them, proof of a material misrepresentation created a presumption that citizenship was procured on that basis. However, the citizen could rebut that presumption by showing that she was actually eligible for citizenship. Justice Brennan wrote a separate concurrence joining in Justice Scalia’s opinion to make a controlling plurality. Justice Brennan’s controlling opinion stressed that citizenship is a “most precious right” and added a more restrictive gloss to Justice Scalia’s view. *Id.*at 783, 108 S.Ct. 1537 (Brennan J., concurring). Although Justice Brennan agreed that a material falsehood can raise a presumption of ineligibility, he said that presumption does not arise unless the government produces evidence sufficient to raise a “fair inference of ineligibility.” *Id.*At the end of the day, then, the government only wins if it shows that the citizen misrepresented a material fact *and*it is “fair to infer that the citizen was actually ineligible.”

*United States v. Latchin,*554 F.3d 709, 713-14 (7th Cir.2009) (citations altered). The Seventh Circuit observed that “[t]his reading of *Kungys*is consistent ... with every federal appellate decision applying *Kungys*to a prosecution under 18 U.S.C. § 1425(a).” Id. at 714 n. 4 (listing cases); see *also, e.g., United States v. Alferahin,*433 F.3d 1148, 1155 (9th Cir.2006) (accept*809ing *Kungys*as applicable to a prosecution under § 1425(a)).

The district court in this case adopted Justice Brennan’s approach, requiring the government to establish “a fair inference that [the] defendant was not eligible for naturalization.” MenSah, however, maintains that *Kungys*is inapposite in criminal eases. He asserts that the governmént’s burden to prove the elements of section 1425(a) beyond a reasonable doubt can be met only with proof that he was in fact ineligible for naturalization when he became a citizen — i.e., the “but for” approach advocated by a minority in *Kungys.*

The distinction Mensah attempts to draw between civil and criminal liability does not work, however, because the Supreme Court has equated the government’s burden of proof .in denaturalization proceedings — the production of “clear, unequivocal and convincing evidence” — with the beyond-a-reasonable-doubt standard of criminal cases:

> [Bjecause of the grave consequences incident to denaturalization proceedings we have held that a burden rests on the Government to prove its charges in such cases by clear, unequivocal and convincing evidence which does not leave the issue in doubt. This burden is substantially identical with that required in criminal cases — proof beyond a reasonable doubt.

*Klapprott v. United States,*335 U.S. 601, 612, 69 S.Ct. 384, 93 L.Ed. 266 (1949) (citation omitted); *see also Kungys,*485 U.S. at 795, 108 S.Ct. 1537 (Stevens, J., concurring in the judgment) (noting that “the factors that support the imposition of so heavy a burden are largely the same in both contexts”). Thus, we are persuaded that the “fair inference” requirement arising from *Kungys*suffices in the criminal context as well. *See Latchin;*554 F.3d at 713 n. 3 (noting that the distinction between the civil and criminal statutes is “trivial” given that “both require a material misrepresentation and procurement of citizenship”).

Importantly, the burden of proving unlawful procurement under the *“Kungys*instruction” remains with the governmént. Here, the jury was told that the government “must prove that if the defendant had provided immigration authorities with truthful information it would have raised a fair inference that [he] was not eligible for naturalization.” The government points out that the court did not tell the jurors to presume ineligibility if the government proved only that he had lied during the naturalization process, thereby creating a mandatory presumption that relieved the government of its burden of proving unlawful procurement. Rather, the instruction properly demanded that the government prove a causative link between Mensah’s lies and his eligibility, albeit at a lower level of certainty than Mensah wanted. As always, of course, the government’s burden is to make the requisite showing beyond a reasonable doubt. In this context, then, the government’s burden was to prove beyond a reasonable doubt that the truthful information would have raised a “fair inference” of ineligibility for naturalization.

Hence, we hold that the district court did not err .in instructing the jury on unlawful procurement.

V.

At the close of the government’s evidence, Mensah moved for judgment of acquittal under Federal Rule of Criminal Procedure 29. He argued, inter alia, that the evidence adduced by the government was insufficient to prove that he (1) made the statements in his naturalization application “under oath,” (2) made a false statement by responding “N/A” when asked if *810he had used other names, and (3) had knowingly committed a crime at the time of his naturalization application and interview. He reiterates each of those contentions on appeal.

We review de novo the district court’s denial of a motion for judgment of acquittal, taking the evidence and all plausible inferences in the light most favorable to the verdict. *United States v. Pérez-Me-léndez,*599 F.3d 31, 40 (1st Cir.2010).

A. “Under Oath”

Mensah’s argument that the government failed to show beyond a reasonable doubt that he had made false statements “under oath” rests on his assertion that the government introduced no evidence that he was given a verbal warning by an official authorized to administer such warnings before he signed his naturalization application. That argument is dispatched by our discussion of the alleged error in the oath instruction. *See supra*Section IV.B.

B. False Statement

Mensah’s attack on the sufficiency of the evidence showing that he made a false statement similarly overlaps with his claim of error in the falsity instruction. He argues that the government produced no evidence that “N/A” was a false response to the “other names” question and asserts that proof that he failed to include information on the form or answered the “other names” question evasively is insufficient to show falsity beyond a reasonable doubt. He points out that Saucier, the immigration official who interviewed him, testified that he did not know what Mensah’s “N/A” notation meant and that he did not ask Mensah for his understanding of the abbreviation.

Our discussion concerning the falsity instruction largely disposes of the sufficiency issue as well. As explained above, a jury may properly find that an incomplete answer to an unambiguous question is false. *See Boskic,*545 F.3d at 86-87. The record amply supports such a finding in this instance, as it was undisputed that Mensah had used another name to apply for a diversity visa. That fact permitted the jury to conclude both that Mensah had falsely asserted that the “other names” question did not apply to him and that he had given a false answer by omitting the true information that he had used the Ap-piah name.

Saucier’s testimony that he did not know how Mensah or his attorney understood “N/A” does not undermine such findings. Mensah offers no interpretation of his own to compete with what we consider the common understanding that “N/A” denotes “not applicable.” Saucier himself understood it that way. He testified that he had placed the same notation on another section of the naturalization form during his interview of Mensah because that section — addressing parents who are United States citizens — was “[n]ot applicable” to Mensah; Hence, based on both Saucier’s testimony and common knowledge, the jurors reasonably could have concluded that “N/A” meant “not applicable,” and that it was a false statement in response to the inquiry about other names used by Men-sah.

C.Knowing Commission of a Crime

Mensah’s conviction under 18 U.S.C. § 1425(a) rests on his having knowingly lied in his citizenship application and interview when he denied that he had committed a crime. On appeal, Mensah argues that the government failed to prove that he knew he had committed a crime at the time he answered the pertinent questions. He specifically challenges the government’s evidence that the Appiah diversity visa application was submitted before he signed his naturalization application in February 2001, emphasizing that the Appi-ah application was undated.

*811This challenge is doubly flawed. First, the evidence presented by the government allowed the jury to conclude that the .Appi-ah diversity application was submitted in October 2000. Although the application itself was undated, the government introduced an envelope addressed to the diversity visa processing center, postmarked October 25, 2000, that bore a return address for Appiah that matched the address on the application. Examining the envelope and application, the jurors reasonably could have concluded that the handwriting on the two documents was similar .and that the two had arrived together. In addition, a government witness testified that the cutoff date to submit applications for the 2002 diversity visa program was early November 2000. This evidence permitted the jury to conclude that Mensah mailed the application in the envelope in October 2000 and, hence, that he had knowingly lied on his naturalization application in February 2001 and in his interview in August 2001 when he denied having committed a crime for which he had not been arrested (i.e., applying for a visa under a false name, in violation of 18 U.S.C. § 1001(a)(2)).21 ■

Second, Mensah does not dispute that he submitted a supplement to the Appiah diversity visa application in June 2001. On the basis of that document alone, the jury could have found that he knowingly lied during his naturalization interview in August 2001 when he denied having committed a crime. Indeed, Mensah’s assertion at the August interview that he had “never” knowingly committed a crime for which he had not been arrested — made after Saucier administered a verbal oath, and with knowledge of the false application — is sufficient evidence to sustain the verdict against each of Mensah’s sufficiency challenges. *See Griffin v. United States,*502 U.S. 46, 59-60, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991) (holding that general verdict stands if the evidence sufficiently supports any of the charged theories of illegal activity); *United States v. Mehanna,*735 F.3d 32, 48 (1st Cir.2013) (same); *United States v. Nieves-Burgos,*62 F.3d 431, 435-36 (1st Cir.1995) (same).22

VI.

Mensah asserts that the district court abused its discretion in allowing the gov-*812eminent to introduce evidence related to his 2006 arrest for acquiring driver’s licenses in two different names. He claims that this evidence, which concerned actions he took years after the charged crime, lacked the “special relevance” necessary to justify its admission and was otherwise inadmissible because it was more prejudicial than probative. *See United States v. Walker,*665 F.3d 212, 228-29 (1st Cir. 2011). He further asserts that the error was not harmless.

A. Background

Federal Rule of Evidence 404(b) generally bars the use of evidence of other crimes or acts to prove “a mere propensity to behave in a certain way,” but permits such evidence where it has “special relevance,” i.e., if it tends to prove such material facts as knowledge, motive or intent. *Walker,*665 F.3d at 229; *see also United States v. Green,*698 F.3d 48, 55 (1st Cir. 2012). Even when other acts evidence would otherwise be admissible under Rule 404(b), however, the court must ensure that its probative value is not substantially outweighed by any unfairly prejudicial effect. *Walker,*665 F.3d at 229; *see also*Fed.R.Evid. 403 (permitting exclusion of relevant evidence if there is a danger of, inter alia, “unfair prejudice, confusing the issues, ... or needlessly presenting cumulative evidence”).

Before trial, the government moved to admit a variety of evidence related to Men-sah’s 2006 arrest. The district court allowed admission of some of the evidence, including the fact of the arrest and the items found in Mensah’s car bearing the Appiah name (a checkbook, an insurance bill, etc.), “for the limited purpose of establishing defendant’s knowledge, motive, intent or lack of mistake” in undertaking the actions charged in this case. The court, however, excluded evidence about the state prosecution itself, deeming it unfairly prejudicial.23

At the request of both parties, the district court instructed the jury on how to view the driver’s license-related evidence:

> The government has offered evidence that Mr. Mensah obtained Massachusetts driver’s licenses in two different names — David Mensah and Willberforce Appiah — and that he was arrested for that offense in 2006. The government also has offered evidence that Mr. Men-sah possessed documents bearing both names at the time of his 2006 arrest.

> The defendant is not on trial for that conduct which occurred years after the events charged in the Indictment. You may not consider that evidence as proof that the defendant has committed the crime charged or as proof that the defendant has a criminal personality or bad character. You may, however, consider the uncharged conduct in determining whether the government has proved beyond a reasonable doubt that in doing the act charged in the Indictment the defendant acted knowingly and intentionally and not because of some mistake, accident or other innocent reason.

On appeal, Mensah reiterates that the government had no legitimate need for the driver’s license evidence, and he argues that its introduction created an “unacceptably high” risk of an impermissible propensity inference, i.e., that he is the type of person who submits fraudulent documents to government agents. In response, the government argues that the evidence *813was important to rebut Mensah’s primary-defense that he did not *knowingly*do anything wrong and, limited in that way, did not risk unfair prejudice.

We review for abuse of discretion a district court’s ruling that evidence may be admitted consistently with Rules 404(b) and 403. *United States v. Appolon,*715 F.3d 362, 373 (1st Cir.2013).

B. Discussion

We are unpersuaded by Mensah’s efforts to wall off his actions to create a second identity in 2001 from the unlawful use five years later of his fraudulently created alter ego, Willberforce Appiah. Mensah’s defense at trial heavily rested on technical arguments about whether he had the requisite knowledge, at the pertinent time, of the criminal nature of his efforts to gain lawful immigrant status in a second name. The evidence that he later secured a fraudulent driver’s license in the Appiah name and that he conducted day-to-day affairs under both names reinforces the inference that he acted in 2001 with the deliberate intent to create a second, false identity and, hence, that he *knowingly*lied when he denied having used other names. Certainly, the district court did not abuse its discretion in seeing such a link and finding that the evidence had probative value.

In so concluding, we do not minimize Mensah’s concern about the jury’s use of the evidence. The charged three-layered immigration crime was complex, and, by contrast, the challenged driver’s license evidence provided straightforward proof that Mensah had unlawfully used two identities on another occasion. The risk of prejudice in the form of an impermissible propensity inference plainly existed.

The district court, however, took steps to limit any such adverse effect, excluding portions of the proffered evidence that it deemed cumulative or unduly prejudicial. Importantly, the court’s cautionary instruction could not have been clearer. It hit all the right notes: emphasizing that Mensah was not on trial for his later conduct, that the 2006 arrest and surrounding circumstances did not prove that he committed the immigration crime, that the evidence of those events was out-of-bounds except on the question of Mensah’s state of mind, and that the government needed to prove beyond a reasonable doubt that the defendant acted knowingly and intentionally. *See United States v. Mare,*668 F.3d 35, 40 (1st Cir.2012) (noting that trial courts will often provide a limiting instruction to minimize the risk that jurors will perceive “multiple-use evidence” as propensity evidence).

It hardly bears repeating that evidence harmful to the defendant is not necessarily *unfairly*prejudicial, *see, e.g., United States v. Williams,*717 F.3d 35, 41 (1st Cir.2013), or that we afford substantial deference to the district court’s judgment that the probative value of evidence is not substantially outweighed by the danger of unfair prejudice, *see, e.g., Mare,*668 F.3d at 39. Here, the court’s careful approach offset the risk of unfair prejudice, and we therefore conclude that its decision to admit certain of the post-2001 evidence was not an abuse of discretion.

VII.

For the reasons that we have explained, each of Mensah’s claims is unavailing. We therefore affirm his conviction.

*So ordered.*,

1

."Diversity visas” are made available to citizens of countries that have been under-represented "within the annual pool of immigrants entering the United States.” *United States v. Kouevi,*698 F.3d 126, 127 (3d Cir.2012); *see also Amouri v. Holder,*572 F.3d 29, 31 (1st Cir.2009); 8 U.S.C. § 1153(c). The visas are distributed by means of an annual lottery held by the Department of State. *Gebre v. Rice,*462 F.Supp.2d 186, 187 (D.Mass.2006) (describing the Diversity Visa Program).

2

. In addition to the application itself, which was undated, the government introduced into evidence an envelope addressed to the Diversity Program, postmarked in October 2000, and bearing a return address in Ghana that included "c/o DK Mensah.” Mensah emphasizes that there is no direct evidence proving that the Appiah application was in the envelope.

3

. In his naturalization application, Mensah reported that he periodically visited family in Ghana.

4

. Such a continuance occurs when a defendant agrees to a period of probation without á guilty finding, and it can lead to dismissal of the case if the defendant adheres to the conditions of probation. *See*Mass. Gen. Laws ch. 278, § 18.

5

. Section 1425(a) provides that "[w]hoever knowingly procures or attempts to procure, contrary to law, the naturalization of any person, or documentary or other evidence of naturalization or of citizenship” is guilty of a crime. 18 U.S.C. § 1425(a).

6

.Section 1015(a) provides that ”[w]hoever 'knowingly makes any false statement under oath, in any case, proceeding, or matter relating to, or under, or by virtue of any law of the United States relating to naturalization, citizenship, or registry of aliens” is guilty of a crime. 18 U.S.C. § 1015(a).

7

. Section 1001(a)(2) imposes a fine or imprisonment, or both, on anyone who "in- any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States, knowingly and willfully ... makes any materially false, fictitious, or fraudulent statement or representation.”

8

. Mensah was not charged with violating section 1015 because the statute of limitations had run on that offense by the time the government completed its investigation.

9

. We note that the *Batson*framework has been extended beyond its original context to cover, inter alia, claims of gender discrimination in jury selection, *see J.E.B. v. Alabama ex rel. T.B.,*511 U.S. 127. 129. 114 S.Ct. 1419. 128 L.Ed.2d 89 (1994), and jury selection in civil cases, *see Edmonson v. Leesville Concrete Co.,*500 U.S. 614, 616, 111 S.Ct. 2077, 114 L.Ed.2d 660 (1991).

10

. The district court did not allow “back strikes,” meaning that counsel could not strike jurors in later rounds that they had accepted in the earlier rounds.

11

. We do not mean to suggest that a *Batson*challenge can succeed only where large numbers of a protected group have been excluded from the jury. Indeed, “ '[t]he Constitution forbids striking even a single prospective juror for a discriminatory purpose[.]’ ” *Snyder,*552 U.S. at 478, 128 S.Ct. 1203 (quoting *United States v. Vasquez-Lopez,*22 F.3d 900, 902 (9th Cir.1994)). Our point is only that small numbers may affect the weight of the numeric evidence, particularly where some of the questioned strikes appear justified by race-neutral reasons.

12

. The government had a total of seven peremptory strikes; the defendant had eleven.

13

. Two potential jurors who had not yet been seated had responded affirmatively when asked to indicate if they had’ such a relationship.

14

. The "question” was in the form of a request for "[ojther names used since you became a permanent resident (including maiden name).”

15

. The absence of such a claim renders inapt his reliance on *Bronston v. United States,*409 U.S. 352, 93 S.Ct. 595, 34 L.Ed.2d 568 (1973), and *United States v. Finucan,*708 F.2d 838 (1st Cir.1983), regardless of whether the literal truth defense articulated in those cases may be "appropriately invoked outside the context of adversary questioning,” *Boskic,*545 F.3d at 92.

16

. For convenience, we repeat here the text of section 1015(a):

> Whoever knowingly makes any false statement under oath, in any case, proceeding, or matter relating to, or under, or by virtue of any law of the United States relating to naturalization, citizenship, or registry of aliens, [is guilty of a crime].

17

. Section 1746, with highlighting reflecting the assumption that an oath may be in writing, states in pertinent part as follows:

> Wherever, under any law of the United States or under any rule, regulation, order, or requirement made pursuant to law, *any matter that is required or permitted to be*supported, *evidenced,*established, or proved *by the*sworn declaration, verification, certificate, statement, *oath,*or affidavit, *in writing*of the person making the same (other than a deposition, or an oath of office, or an oath required to be taken before a specified official other than a notary public), such matter may, with like force and effect, be supported, evidenced, established, or proved by the unsworn declaration, certificate, verification, or statement, in writing of such person which is subscribed by him, as true under penalty of perjury, arid dated. ...

18

. *Black's*defines an "affirmation” as “[a] pledge equivalent to an oath but without reference to a supreme being or to 'swearing.' " *Black’s Law Dictionary*64. Under federal law, reference to an oath includes an affirmation. *See*1 U.S.C. § 1.

19

. As the government points out, Mensah did make at least one false statement subject to a verbal oath. Saucier, the immigration officer, administered an oath at the outset of Mensah’s naturalization interview. Mensah stated during that interview that he had never knowingly committed a crime for which he had not been arrested.

20

. The statute at issue in *Kungys*wqs a civil provision, 8 U.S.C. § 1451(a), which requires revocation of citizenship when naturalization was "illegally procured or [was] procured by concealment of a material fact or by willful misrepresentation." As noted above, the criminal statute at issue here provides that "[w]hoever knowingly procures or attempts to procure, contrary to law, the naturalization of any person, or documentary or other evidence of naturalization or of citizenship” is guilty of a crime. 18 U.S.C. § 1425(a).

21

. The government also states that, although the envelope and application bore different tracking numbers, both numbers were stamped on the backside of the one-page application. As Mensah points out, there is no evidence in the record that the document bearing only the two numbers is a copy of the reverse side of the single-page diversity visa application. Nonetheless, the page was included in the Appiah immigration file, and the jury could have inferred from the juxtaposition of the two numbers that the processing center viewed the envelope and application as related.

22

. Mensah made a different "knowledge” argument before the district court, pointing to a lack of proof that he knew it was a crime to apply for a diversity visa under a false name (knowledge necessary to support a finding that he knowingly lied when he said he had never committed a crime for which he had not been arrested, in violation of section 1015(a)). Mensah also argued to the district court that the evidence failed to show that he knew he was procuring naturalization "contrary to law,” a prerequisite for conviction under section 1425(a). Mensah resuscitates the first of these contentions in his reply brief and makes a passing reference to the latter in his opening brief. Neither warrants our attention. *See United States v. Newell,*658 F.3d 1, 34 (1st Cir.2011) (noting that "issues raised for the first time in an appellant's reply brief are generally deemed waived” (internal quotation marks omitted)); *United States v. Espinal-Almeida,*699 F.3d 588, 599 n. 9 (1st Cir.2012) (noting that "issues that are adverted to in a perfunctory manner absent developed argumentation are waived” (internal quotation marks omitted)).

23

. The court also excluded other evidence that the government sought to use, including materials in the Appiah immigration file and documents seized from Mensah during an airport inspection in 2008.