
521 F.3d 877 (2008)
UNITED STATES of America, Appellee,
v.
Harley TYNDALL, Appellant.
No. 07-2131.
United States Court of Appeals, Eighth Circuit.
Submitted: December 12, 2007.
Filed: April 4, 2008.
*878 *879 *880 Denise Ellen Frost, argued, Omaha, NE, for appellant.
Robert Francis Cryne, AUSA, argued, Douglas R. Semisch, AUSA, on the brief, Omaha, NE, for appellee.
Before LOKEN, Chief Judge, WOLLMAN, and SHEPHERD, Circuit Judges.
WOLLMAN, Circuit Judge.
Harley Tyndall was convicted by a jury of sexual abuse of a minor in violation of 18 U.S.C. § 2243(a). He was acquitted of engaging or attempting to engage in a sexual act with a person who was physically incapable of consenting in violation of 18 U.S.C. § 2242(2). He was sentenced to 120 months' imprisonment and now appeals, contending that the district court[1] erred in denying his motions for acquittal, mistrial, and new trial, as well as in imposing sentence. We affirm.

I.
Megana Rivera and her husband, Robert, who is Tyndall's cousin, live in Walthill, Nebraska, on the Omaha Nation Indian Reservation. In the early morning hours of February 5, 2006, Tyndall and Megana returned after a night of dancing and drinking to Megana's home, where they continued to consume alcohol. Robert, who was working his night shift, was not present. Megana had hired her 15-year-old cousin M.R., her regular babysitter, to babysit her two small children while she was out. M.R. was encouraged to join Tyndall and Megana in a drinking game that left M.R. vomiting and passing in-and-out of consciousness. Upon regaining consciousness, M.R. went to a spare bedroom, where she fell asleep.
According to Tyndall's testimony, a highly intoxicated Megana grabbed his crotch as he was about to leave, causing him extreme pain because of a cut on his penis that he had recently suffered. He went to the bathroom and discovered that the cut had been opened and was bleeding, resulting in some blood on his underwear and hands. He did not refasten his pants because doing so put too much pressure on his injured penis. From the spare bedroom across the hall from the bathroom, M.R. called him into the room and told him she wanted to "get" with him, whereupon they kissed consensually. Tyndall testified that although M.R. pulled his hand to her crotch, he did not penetrate any part of her genital area. Recalling M.R.'s age, he pushed her away and then went into the living room, where he decided to wait for Robert to return to the home so that he could explain what had happened. Megana entered the living room and asked what Tyndall had done to M.R. He tried to explain that nothing had occurred because his injury, which he then showed to Megana, was too painful to permit sexual intercourse. Megana ordered him out of the home and then called the tribal police.
M.R. testified that the next thing that she remembered after falling asleep was regaining consciousness long enough to see Tyndall between her legs and to feel pressure *881 in her vagina, after which she again passed out. After regaining consciousness, she was asked by Megana why she was wearing only a shirt and what Tyndall had done to her.
Megana testified that she had ordered Tyndall to leave, whereupon he showed her his injury. She then helped M.R. to the bathroom, where she told M.R. to sit on the toilet and wipe herself. Megana observed that the toilet paper M.R. used had blood on it, whereupon M.R. began to cry and flushed the toilet paper away. Megana then called the tribal police.
The medical examination of M.R. revealed no evidence of trauma, bruises, scrapes, or abrasions that would indicate sexual activity, and her hymen was still intact. The examining doctor testified that these results were not uncommon in sexual assault victims and that they did not rule out the possibility of sexual activity. M.R.'s period had ended days earlier. A rape kit examination revealed the existence of a bacteria called ureaplasma, which is passed almost exclusively by sexual contact. M.R. testified that she had never had sexual intercourse before the incident with Tyndall. M.R.'s DNA was found on Tyndall's underwear.
Investigating officer Bernard Morris testified on cross-examination that he saw a piece of tissue paper with blood on it in the bathroom. On redirect examination, he testified that there was no bloody tissue included with the evidence gathered at the scene, and that what he had really seen was a bloody carpet fiber. On recross examination, he testified that what he saw was a bloody tissue, perhaps in the wastebasket. On the second redirect examination, he again stated that what he saw was bloody carpet fibers, not tissues. He testified that all relevant evidence had been collected and turned over to the FBI. No bloody tissue appeared in any police photograph taken that night. No other officer saw the alleged tissue paper, and none was ever logged as evidence.

II.
Tyndall contends that the prosecution's failure to disclose the fact of Officer Morris's belief in the existence of a bloody tissue paper constituted a violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), that entitles him to a new trial.
We review for abuse of discretion the denial of a motion for a mistrial, United States v. Gray, 369 F.3d 1024, 1027 (8th Cir.2004), as we do a denial of a motion for a new trial based on a Brady violation. United States v. Haskell, 468 F.3d 1064, 1075 (8th Cir.2006). We review de novo a denial of a motion for a judgment of acquittal. United States v. Stanko, 491 F.3d 408, 411 (8th Cir.2007).
The Supreme Court held in Brady that "the suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution." 373 U.S. at 87, 83 S.Ct. 1194. Brady is violated if three requirements are met: "The evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently; and prejudice must have ensued." Morales v. Ault, 476 F.3d 545, 554 (8th Cir.2007) (quoting Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)). The evidence is not material and no prejudice can be shown unless there is a reasonable probability that the verdict would have been different if the evidence had not been suppressed. Morales, 476 F.3d at 554; Johns v. Bowersox, 203 F.3d *882 538, 545 (8th Cir.2000). A prosecutor has a duty to disclose evidence known by police officers, even if not known by the prosecutor, because a prosecutor has a duty to learn of such information. Strickler, 527 U.S. at 280-81, 119 S.Ct. 1936. The underlying question is whether the verdict is worthy of confidence. United States v. Almendares, 397 F.3d 653, 664 (8th Cir.2005). A mid-trial disclosure violates Brady only if it comes too late for the defense to make use of it. Id.
Tyndall argues that the existence of a bloody tissue would support his contention that his penis was so severely injured that he would not have engaged in sexual activity. Because there appears to be no question that Tyndall had such an injury, however, and that he was bleeding from it that night, the effect of this evidence would have been cumulative, at best. Accordingly, we conclude that-there is no reasonable probability that the verdict would have been different if Tyndall had known before trial that Officer Morris thought he saw a tissue with blood on it in Megana's bathroom.
Additionally, the disclosure was not so untimely that Tyndall could not make use of it at trial. The district court granted an extended period of cross- and redirect examination on this subject, and Tyndall does not provide any reason to believe that further cross-examination of any witnesses could have aided his cause. Indeed, Tyndall did not request to recall for further cross-examination the officer who had testified prior to Officer Morris's testimony. Tyndall argues that he would have been able to impeach M.R.'s and Megana's testimony that M.R. had flushed the bloody toilet paper that she had used to wipe herself after the incident by proving that she had actually disposed of that tissue in the wastebasket. Even if Tyndall had obtained the maximum impeachment value from such testimony, however, it would not have created a reasonable probability of a different outcome. Accordingly, the district court did not err in denying his motions for a new trial, a mistrial, and a judgment of acquittal.

III.
Tyndall argues that the district court erred in several respects in imposing sentence. "We review the district court's conclusions of law and application of the sentencing guidelines de novo. We review factual findings for clear error." United States v. Fields, 512 F.3d 1009, 1011 (8th Cir.2008) (internal citation omitted). We give great deference to a district court's determination of a witness's credibility, United States v. Denton, 434 F.3d 1104, 1114 (8th Cir.2006), and to its decision to enhance a sentence for obstruction of justice. United States v. Frank, 354 F.3d 910, 923 (8th Cir.2004).

A.
The district court increased Tyndall's offense level for obstruction of justice after finding that he had committed perjury. To apply this enhancement, the district court was required to have found by a preponderance of the evidence that Tyndall willfully gave false testimony on a material matter. United States Sentencing Guidelines (U.S.S.G.) § 3C1.1; United States v. Dunnigan, 507 U.S. 87, 94, 113 S.Ct. 1111, 122 L.Ed.2d 445 (1993); United States v. Ziesman, 409 F.3d 941, 956 (8th Cir.2005). The bare fact of conviction following the defendant's testimony is insufficient to support an obstruction of justice enhancement. United States v. Abdul-Aziz, 486 F.3d 471, 478-79 (8th Cir.2007). A district court's failure to expressly find willfulness in giving false testimony is not grounds for reversal if the evidence of willfulness is unequivocal and the defendant's contradictory testimony is not a result *883 of confusion, mistake, or faulty memory. United States v. Brown, 311 F.3d 886, 890 (8th Cir.2002); United States v. Esparza, 291 F.3d 1052, 1055 (8th Cir.2002).
The district court found that Tyndall's testimony was not credible and that Megana's and M.R.'s testimony was credible. The willful falseness of Tyndall's testimony is rendered unequivocal from the evidence that M.R. was discovered to have a sexually transmitted bacteria despite her testimony that she had never before engaged in sexual activity, the lack of any medical evidence of any trauma to M.R. that would cause bleeding and the presence of blood visible on a tissue that M.R. used to wipe herself, along with the presence of M.R.'s DNA on Tyndall's underwear. Based on this evidence, the district court did not clearly err in finding Tyndall's testimony not credible and did not err by enhancing his offense level for obstruction of justice. That said, we once again emphasize the importance of detailed findings to the effect that the defendant testified falsely about a material matter" with a willful intent to deceive the factfinder. United States v. Molina, 172 F.3d 1048, 1058 (8th Cir.1999). See also, e.g., Abdulr-Aziz, 486 F.3d at 478-79.
Likewise, the district court did not err in refusing to grant Tyndall an offense-level reduction for acceptance of responsibility pursuant to U.S.S.G. § 3E1.1. See United States v. Vaca, 289 F.3d 1046, 1048 (8th Cir.2002). It is rarely appropriate to grant a reduction for acceptance of responsibility to a defendant whose offense level has been increased for obstruction of justice. U.S.S.G. § 3E1.1 cmt. n. 4. There is no special circumstance in this case that warrants granting such a request. Further, a reduction for acceptance of responsibility is not appropriate if the defendant demands a trial at which he denies the "essential factual elements of guilt." U.S.S.G. § 3E1.1 cmt. n. 2; see United States v. Williams, 486 F.3d 377, 383 (8th Cir.2007), vacated, ___ U.S. ___, 128 S.Ct. 882, 169 L.Ed.2d 718 (remanding for resentencing in light of Kimbrough v. United States, ___ U.S. ___, 128 S.Ct. 558, 169 L.Ed.2d 481 (2007)).

B.
The district court did not err in calculating the base offense level as 30 under U.S.S.G. § 2A3.1 rather than as level 18 under U.S.S.G. § 2A3.2. Tyndall was convicted of sexual abuse of a minor in violation of 18 U.S.C. § 2243(a), which would normally result in a base offense level of 18 under U.S.S.G. § 2A3.2. A cross-reference in U.S.S.G. § 2A3.2(c), however, requires the application of U.S.S.G. § 2A3.1 if conduct proscribed under 18 U.S.C. § 2242 is a part of the offense. Tyndall was acquitted of the charges under § 2242, which forbids "engag[ing] in a sexual act with another person if that other person is . . . incapable of appraising the nature of the conduct [] or . . . physically incapable of declining participation in, or communicating unwillingness to engage in, that sexual act." Nevertheless, a district court may use a defendant's relevant conduct in sentencing if it finds by a preponderance of the evidence that the conduct occurred, even if that conduct formed the basis of a criminal charge on which a jury acquitted the defendant. United States v. Watts, 519 U.S. 148, 156-157, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997); United States v. No Neck, 472 F.3d 1048, 1055 (8th Cir.2007); United States v. High Elk, 442 F.3d 622, 626 (8th Cir.2006); U.S.S.G. § 6A1.3 cmt.; see U.S.S.G. § 1B1.3(a)(1)(A). The district court found by a preponderance of the evidence that Tyndall's conduct violated 18 U.S.C. § 2242 because M.R.'s inebriated state made her incapable of appraising the nature of the sexual act and physically incapable of refusing or communicating *884 her refusal to participate in the sexual act. Thus, the application of the cross-reference to U.S.S.G. § 2A3.1 was appropriate.
Tyndall argues that because the disparity in sentencing ranges is so great, the district court should have been required to find that there was clear and convincing evidence of the existence of the relevant conduct relied upon to enhance the sentence. Both this court and the Supreme Court have recognized that due process might require proof beyond a mere preponderance of the evidence if an extreme increase in the applicable sentencing range results from the consideration of relevant conduct. See Watts, 519 U.S. at 156 & n. 2, 117 S.Ct. 633; United States v. Toumley, 929 F.2d 365, 369 (8th Cir.1991). We indicated, without so holding, in Townley that a seven-fold increase in the permissible sentencing range might require the application of the clear and convincing standard of proof as a prerequisite to the consideration of relevant but unconvicted conduct. 929 F.2d at 369-70. We have twice held that a four-fold increase in the permissible sentencing range does not require the use of the clear and convincing evidence standard. See United States v. Bradford, 499 F.3d 910, 920 (8th Cir.2007); United States v. Alvarez, 168 F.3d 1084, 1088 (8th Cir.1999).
If the relevant acquitted conduct is not considered, Tyndall's base offense level would be 18, plus a two-level enhancement for obstruction of justice (but no increase for the age of the victim, which is accounted for in U.S.S.G. § 2A3.2). At criminal history category III, Tyndall would be subject to a 51-month prison sentence. The sentencing range for offense level 34 in criminal category III rises to 235 months, limited by the statutory maximum under 18 U.S.C. § 2243(a) of 180 months, which would be about three-and-a-half times greater than 51 months, less than the increase in Bradford and Alvarez. Accordingly, we conclude that an increase of this magnitude is not so extreme as to require that the district court find the existence of relevant conduct to have been established by clear and convincing evidence rather than by a preponderance of the evidence.
Finally, the district court did not err in increasing Tyndall's offense level on the basis of M.R.'s age. Normally, the applicable section of the guidelines for a violation of 18 U.S.C. § 2243(a) is U.S.S.G. § 2A3.2, in which the victim's age is already considered, so no further enhancement for the victim's age would be appropriate. When the cross-reference found in U.S.S.G. § 2A3.2(c) is applied, however, U.S.S.G. § 2A3.1 is the relevant section. This section's base offense level does not contemplate that the victim is a minor and states that the offense level should be increased by two if the victim is at least twelve but less than sixteen years old. U.S.S.G. § 2A3.1(b)(2)(B). Because M.R. was fifteen years old at the time of the incident, the district court correctly increased the offense level by two.
The judgment is affirmed.
NOTES
[1]  The Honorable Laurie Smith Camp, United States District Judge for the District of Nebraska.
