COLLOTON, Circuit Judge.

Robert Raymond Tail was convicted by a jury of two counts of sexual abuse and two counts of sexual abuse of a minor in violation of 18 U.S.C. §§ 2242(1) and 2243. He appeals, and we affirm.

I.

J.H. and M.H. were foster children who were placed with Robert Tail and Tail's wife, Vanessa, in early 2003. J.H., then fifteen years old, and M.H., then thirteen, are first cousins to Vanessa. At trial, the government presented evidence that Tail entered a bedroom and sexually abused J.H. in March 2003. M.H. similarly testified that sometime after the incident with J.H., around April 2003, Tail entered a room where M.H. was sleeping and abused her as well, threatening to "do it again" if she told anyone about the abuse. The girls' grandfather, Percy White Plume, testified that he had confronted Tail about the abuse and Tail responded, "I'm sorry I did that. . . . I'm sorry I did that to them." (T. Tr. at 292). J.H. also testified that on May 24, 2003, on a trip to Rapid City, she awoke to find Tail raping her. J.H. reported the incident to her high school counselor, and Tail was subsequently arrested on federal sexual abuse charges. Tail was charged in South Dakota state court with raping J.H. in May, and he was convicted. He was later indicted in federal court for two counts of sexual abuse and two counts of sexual abuse of a minor arising out of the March and April incidents with J.H. and M.H.

On April 7, 2004, while in custody, Tail was transported from the Pine Ridge Jail to the Rapid City federal courthouse by Special Agent Richard Lauck of the FBI. During the almost two-hour drive, Tail and Lauck engaged in conversation. During the conversation, Tail commented that he hoped his family would wait for him while he was in prison, and that he wanted Agent Lauck to visit him while he was in prison. Tail later moved to suppress the statements, arguing that they were the product of an interrogation by Agent Lauck that was not preceded by warnings as required by Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). The district court denied the motion.

Prior to trial, Tail also sought an order permitting him to introduce evidence that J.H. and M.H. had made prior allegations of sexual abuse against others, and additional evidence that J.H. had tested positive for Hepatitis B while Tail had tested negative for the disease. Both of these motions were denied. The district court found that the prior allegations were not demonstrably false, and that admission of the evidence was therefore not required by the Confrontation Clause and was inadmissible under Federal Rule of Evidence 412, which bars admission of a victim's prior sexual acts under most circumstances, and under Federal Rule of Evidence 403. As for the Hepatitis B diagnosis, the court found that this was also evidence of sexual behavior properly excluded under Rule 412. The government subsequently moved in limine to exclude any reference to the Hepatitis B diagnosis, and at a hearing, a pediatrician testified that it was likely that J.H. acquired the disease when she was under the age of five, and also fairly unlikely that a chronic carrier such as J.H. would pass the disease to another person through sexual contact. Based on this information, the court determined that the evidence had minimal probative value that was outweighed by the danger of unfair prejudice.

Tail also filed a motion in limine asking the court to exclude any references to his prior state court conviction for the second degree rape of J.H., arguing that the conviction was irrelevant and extremely prejudicial. The district court denied this motion, finding that the evidence was admissible as a prior sexual assault offense under Federal Rule of Evidence 413. The court thought the evidence was highly probative and that it should not be excluded under Rule 403, but gave a cautionary instruction to the jury at trial.

The jury found Tail guilty of all four charged offenses. For each of the two charges of sexual abuse of a minor, the district court sentenced Tail to 240 months' imprisonment, with the sentences to run concurrently. Tail was sentenced to an additional 120 months for each of the sexual abuse charges, with those sentences running concurrently with each other but consecutive to the sentences imposed for sexual abuse of a minor.

II.

On appeal, Tail renews his challenge to the district court's denial of his motion to suppress the statements that he made during a car ride with Agent Lauck. His argument is based on the requirement that an officer give Miranda warnings when a suspect is interrogated while in custody. Rhode Island v. Innis, 446 U.S. 291, 300, 100 S.Ct. 1682, 64 L.Ed.2d 297 (1980). There is no dispute here that Tail was in custody, but the district court concluded that Tail was not under interrogation when the statements were made. We review the district court's factual findings for clear error and its legal conclusions de novo. United States v. Londondio, 420 F.3d 777, 783 (8th Cir. 2005).

"Voluntary statements that are not in response to interrogation are admissible with or without the giving of Miranda warnings." Id. "Interrogation" includes express questioning, and it also extends to "words or actions on the part of the police (other than those normally attendant to arrest and custody) that the police should know are reasonably likely to elicit an incriminating response from the suspect." Innis, 446 U.S. at 301, 100 S.Ct. 1682 (footnote omitted). Tail argues that Agent Lauck intentionally "gained Tail's trust" and "engage[d] [Tail] in friendly conversation," knowing that Tail was "especially vulnerable," and then "took advantage of Tail's vulnerability" by recording his statements on a piece of paper that he kept in the van. (Appellant's Br. at 14-15).

The district court found Agent Lauck's account of the car ride, which involved "minimal, but polite conversation," to be credible, and we see no clear error in that determination. There is no suggestion that Agent Lauck asked Tail any questions or steered the conversation toward potentially incriminating topics. To the contrary, Lauck testified that he intentionally avoided questioning Tail and kept his own answers to Tail's questions short. Polite conversation is not the functional equivalent of interrogation. Londondio, 420 F.3d at 783; United States v. Fleck, 413 F.3d 883, 893 (8th Cir. 2005). Tail also makes something of the fact that Agent Lauck kept a clipboard in the van to record his incriminating statements. Lauck testified that he kept the clipboard for a variety of purposes, including recording his mileage and other data about his trip, but even if he kept the clipboard for the sole purpose of recording Tail's statements, that would not transform the encounter into an interrogation. We therefore conclude that the district court properly denied the motion to suppress.

III.

Tail also challenges three of the district court's evidentiary rulings. He argues that the district court abused its discretion in admitting evidence of his prior state court conviction for second degree rape. He also contends that the court erred in excluding evidence that J.H. had tested positive for Hepatitis B and that she and M.H. had previously made false allegations of abuse.

A.

Tail concedes that his conviction for second degree rape qualifies as an "offense of sexual assault" under Rule 413(d)(2), which provides that evidence of such crimes is admissible in sexual assault trials and may be considered "for its bearing on any matter to which it is relevant." Fed.R.Evid. 413(a). Tail argues that the evidence should nonetheless have been excluded under Rule 403, because its probative value was substantially outweighed by the danger of unfair prejudice, and under Rule 404(b), because it was impermissible character evidence.

We give "great deference to the district court's balancing of the probative value and the prejudicial impact," United States v. Looking Cloud, 419 F.3d 781, 785 (8th Cir. 2005), and we see no abuse of the court's discretion in this case. The conviction was probative because it involved the same victim and an act that occurred close in time and under circumstances similar to the crime charged in this case. See United States v. Medicine Horn, 447 F.3d 620, 623 (8th Cir. 2006). The evidence was "prejudicial" in the sense that it tended to suggest that Tail had a propensity to commit sexual assaults, but this does not constitute unfair prejudice. Id. To require the exclusion of this evidence based on the asserted "inflammatory nature" of sexual offenses would be at odds with the "strong legislative judgment" in favor of admitting such evidence that Congress expressed in adopting Rule 413. Id.; see also United States v. LeCompte, 131 F.3d 767, 770 (8th Cir. 1997).

Tail also argues that Rule 404(b) requires exclusion of the conviction, but the policy articulated in Rule 413, unique to cases involving sexual assaults, renders the general prohibition on propensity evidence in Rule 404(b) inapposite. See United States v. Mound, 149 F.3d 799, 802 (8th Cir. 1998). In addition, in this case the district court issued an instruction advising the jury that the evidence was received for "a limited purpose only," and that the prior conviction "does not mean that he is guilty of the charges of sexual abuse and sexual abuse of a minor as to which he has pleaded not guilty in this case." (R. Doc. 167, Jury Instruction No. 8). Such cautionary instructions decrease any danger of unfair prejudice. United States v. Crawford, 413 F.3d 873, 876 (8th Cir. 2005). Under these circumstances, we do not believe the district court abused its discretion in admitting the evidence of Tail's prior conviction.

B.

Tail also contends that the district court abused its discretion in excluding evidence that J.H. had tested positive for Hepatitis B. Because Hepatitis B is sometimes acquired through sexual contact, Tail urged the district court to admit this evidence to impeach J.H.'s testimony that she had no other sexual partners. Tail also proffered evidence that he had tested negative for Hepatitis B, and argued that his negative test results tended to rebut an inference that he was the source of any sexual injuries or physical evidence. Tail now concedes that the evidence was inadmissible for impeachment purposes, see Fed.R.Evid. 412; see also United States v. White Buffalo, 84 F.3d 1052, 1053-54 (8th Cir. 1996), but contends that the evidence was nonetheless admissible as substantive evidence to prove that "a person other than the accused was the source of semen, injury, or other physical evidence." Fed.R.Evid. 412(b)(1)(A). The physical evidence to which Tail believes his test results are relevant is the testimony of a midwife who examined J.H. in May 2003 and found bruising and lacerations.

The exception to the general prohibition on admission of a victim's past sexual behavior permits only the introduction of "specific instances of sexual behavior," and Tail has not offered any such "specific instance" to show an alternative source of physical evidence. See Fed.R.Evid. 412. Even if he had, however, the evidence is not relevant in the way that he suggests. The government did not introduce evidence of J.H.'s Hepatitis B, so Tail's negative test results cannot rebut an inference that he was the cause of her disease. Tail's alternative contention that the test results prove that another man caused the "physical evidence" gathered from J.H.'s body relies on an inference that J.H. must have contracted the disease from other sexual contact, and that this other sexual contact could also have been the cause of bruising and lacerations on her body. But the evidence produced at the pre-trial hearing did not support the assumption that J.H.'s Hepatitis B was acquired through another recent sexual encounter. Instead, the uncontroverted testimony of a pediatrician, Dr. Lori Strong, was that Hepatitis B can be contracted from non-sexual sources, and that because J.H. was in a chronic carrier stage of the disease, it was most likely that she contracted the disease before the age of five. Tail did not rebut this evidence, and the district court did not abuse its discretion by finding that the Hepatitis B results were not sufficiently probative to be admissible.

C.

Tail's final evidentiary challenge is to the exclusion of evidence that he believes would demonstrate that J.H. and M.H. previously made false allegations concerning sexual abuse. Although impeaching a witness's character for truthfulness is not a recognized exception to Rule 412's general prohibition on evidence of sexual history, United States v. Withorn, 204 F.3d 790, 795 (8th Cir. 2000), Tail argues that false allegations do not constitute "evidence of a victim's past sexual behavior" that is barred by Rule 412. Alternatively, he contends that Rule 412 must give way to the protections of the Confrontation Clause of the Constitution, and that exclusion of the evidence violated his rights under the Sixth Amendment. See Fed.R.Evid. 412(b)(1)(C). The district court refrained from deciding whether the evidence would constitute protected sexual history under Rule 412, observing that the Confrontation Clause analysis would be the same in either event. The court concluded that none of the allegations cited by Tail was demonstrably false, and that the allegations therefore had minimal probative value that was outweighed by other concerns.

A primary interest secured by the Confrontation Clause is the right of cross-examination. The opportunity to expose "possible biases, prejudices, or ulterior motives" of a witness, as "they may relate directly to the issues or personalities in the case at hand," is one important function of the right to confront witnesses. Davis v. Alaska, 415 U.S. 308, 316, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). Thus, the Confrontation Clause may require the admission of certain evidence otherwise excluded by the rules of evidence, but it is clear that not all evidence that is "the least bit probative of credibility" must be admitted. United States v. Bartlett, 856 F.2d 1071, 1088 (8th Cir. 1988); see also Davis, 415 U.S. at 321, 94 S.Ct. 1105 (Stewart, J., concurring). As pertinent here, we have held that in a sexual abuse case, evidence alleging that the accuser made prior false accusations may be excluded if the evidence has minimal probative value. Bartlett, 856 F.2d at 1089; White Buffalo, 84 F.3d at 1054. And the propriety of excluding such evidence is strengthened where the prior incident is unrelated to the charged conduct, and where the defendant intends to use the evidence as part of an attack on the "general credibility" of the witness. Bartlett, 856 F.2d at 1088.

Tail sought to introduce evidence of prior allegations of abuse that he claimed were made falsely by J.H. The first allegation was purportedly directed toward an individual named Darwin Apple, whom Tail claimed had been accused of sexual abuse in 2003. Tail substantiated this claim by producing a statement of Vanessa Tail that conveyed the girls' assertions that Apple's wife had physically mistreated them, and that Apple had pushed M.H. off the couch and hit her with a pillow. Tail did not produce evidence that the girls made allegations of sexual abuse, or that the report of physical abuse resulted in any investigation or charges. He presented no evidence of a denial by Apple. The evidence thus did not support Tail's claim that J.H. and M.H. even accused Apple of sexually abusing the girls, much less the assertion that the witnesses made false accusations. The Confrontation Clause did not require admission of this evidence.

Tail's other allegations of prior false accusations were based on a report of J.H.'s grandmother, Mary Johnson. According to a report of an interview with Johnson conducted by Tail's investigator, Johnson said that J.H. accused Johnson's son, Frank, and Johnson's boyfriend, Jesse Fabian Ortega, of molesting J.H. To support the latter allegation, Tail offered a report of an interview of J.H. at a child advocacy center in May 2002, in which J.H. was reported as saying that Ortega had pulled down her underwear and touched her inappropriately. Tail also presented a one-page excerpt from a transcript of a state court proceeding in which J.H. acknowledged that she had "some problem" with Ortega, and contacted law enforcement about it. In an effort to show that J.H. made accusations that were false, Tail pointed to the fact that Johnson reportedly said she "was always around and knew nothing had happened" with Ortega or Frank Johnson. Tail also presented testimony from his investigator that Ortega, when approached by the investigator, had denied touching J.H. inappropriately.

The district court concluded that the allegations concerning Ortega and Frank Johnson had minimal probative value, and that the danger for unfair prejudice, confusion of the issues, and misleading the jury substantially outweighs the minimal probative value of the evidence. The court reasoned that Ortega had a motive to lie, because agreement with J.H.'s allegation would have constituted an admission that he committed a federal crime. The court accurately observed that "we are left with bare allegations from both sides and no firm proof of the falsity of J.H.'s allegation." (R. Doc. 127, at 8). As for Frank Johnson, Tail did not even offer proof that Johnson himself ever denied the proffered allegation.

We agree with the district court that the Confrontation Clause does not mandate the admission of this evidence, because it had only limited probative value. The evidence of falsity is weak, and there is no substantial showing that J.H.'s allegations against Tail are part of a broader scheme involving contrived allegations against Ortega and Frank Johnson, or that they shared a common motivation. Cf. United States v. Stamper, 766 F.Supp. 1396, 1402-03 (W.D.N.C. 1991), aff'd sub nom. In re One Female Juvenile Victim, No. 91-5334, 1992 WL 63334 (4th Cir. Apr.1, 1992) (unpublished). Admission of this evidence would have triggered mini-trials concerning allegations unrelated to Tail's case, and thus increased the danger of jury confusion and speculation. See Withorn, 204 F.3d at 795; see also Fed.R.Evid. 403. The district court's ruling was consistent with our guidance in Bartlett, 856 F.2d at 1089, and White Buffalo, 84 F.3d at 1054, and we discern no error.

IV.

Finally, Tail argues that his Fifth Amendment rights were violated by his conviction under two different statutes for the same conduct. Tail was convicted of both sexual abuse, 18 U.S.C. § 2242(1), and sexual abuse of a minor, 18 U.S.C. § 2243(a), with respect to each victim. He argues that because all four convictions arose out of the same two acts, punishment under both statutes violates his right to be free from double jeopardy.

We conclude that there was no violation of the Double Jeopardy Clause. "[M]ultiple punishments are permitted for separate convictions when each requires an element of proof that the other does not." United States v. Beltz, 385 F.3d 1158, 1161 (8th Cir. 2004); see also Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 76 L.Ed. 306 (1932). The offense of sexual abuse has as an element the act of "threatening or placing . . . [a] person in fear," 18 U.S.C. § 2242(1), which is not shared by sexual abuse of a minor. Sexual abuse of a minor also has a distinct element, because it requires proof that the victim was at least 12 but not yet 16 years old and was at least four years younger than the perpetrator. 18 U.S.C. § 2243(a). Thus, Tail's double jeopardy rights were not infringed by his punishment for the violation of both statutes.

Our court has rejected Tail's argument that a single course of conduct can lead to only one conviction, United States v. Boykins, 966 F.2d 1240, 1245 (8th Cir. 1992), and Tail's reliance on United States v. Chipps, 410 F.3d 438 (8th Cir. 2005), does not call for a different conclusion here. Chipps involved a defendant who was convicted on two counts of violating one statute. In finding the defendant's convictions to be multiplicitous, we considered whether his offenses had arisen from the same "impulse," because Congress had not specified a different unit of prosecution that would otherwise make the two convictions distinct. Id. at 449. Here, by contrast, Congress has made clear that "sexual abuse" and "sexual abuse of a minor" are distinct crimes with separate punishments by defining them to include different elements of proof.

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The judgment of the district court is affirmed.