Full opinion text
REENA RAGGI, Circuit Judge: In 2008, former high school athletic coach Todd J. Broxmeyer was found guilty after a jury trial in the United States District Court for the Northern District of New York (Thomas J. McAvoy, Judge) of two counts of producing child pornography, see 18 U.S.C. § 2251(a) (Counts One and Two); one count of attempting to produce child pornography, see id. § 2251(a), (e) (Count Three); one count of transporting a minor across state lines with the intent to engage in criminal sexual activity, see id. § 2423(a) (Count Four); and one count of possessing child pornography, see id. § 2252A(a)(5)(B) (Count Five). The victims of all these crimes were teenage girls under Broxmeyer’s purported tutelage and care. On Broxmeyer’s first appeal, this court reversed his convictions on Counts One, Two, and Four. See United States v. Broxmeyer, 616 F.3d 120 (2d Cir.2010). As to the first two counts, the court concluded that the evidence was insufficient as a matter of law to permit the jury to find that Broxmeyer had solicited the production of — rather than simply received — the two images of child pornography at issue. See id. at 124-27. As to Count Four, the court, by a divided vote, concluded that Broxmeyer’s interstate transportation of a 15-year-old girl after compelling her to engage in sodomy could not support a conviction for interstate transportation of a minor with intent to engage in criminal sexual activity, that object already having been achieved before the defendant crossed any state border. See id. at 128-30; see also id. at 130 (Wesley, J., dissenting in part). Vacating Broxmeyer’s original 40-year prison sentence, this court remanded for resentencing on the remaining two counts of conviction for possession and attempted production of child pornography. See id. at 130. Broxmeyer now appeals from so much of the amended judgment entered on December 29, 2010, as sentenced him to concurrent prison terms of 30 years on Count Three’s attempted production charge and 10 years on Count Five’s possession charge. He argues that the sentence is infected by various procedural errors and, in any event, that 30 years’ incarceration is substantively unreasonable in his case. Indeed, Broxmeyer maintains' — -and our dissenting colleague agrees — that any sentence higher than the minimum 15-year prison term mandated for Count Three, see 18 U.S.C. § 2251(e), would be substantively unreasonable. We reject both arguments as without merit. I. Background A. The Conduct Informing the Challenged Sentence Precisely because Broxmeyer and the dissent maintain that only the mandated minimum sentence for Count Three can be substantively reasonable in this case — in short, that the district court effectively had no sentencing discretion whatsoever — it is necessary to set forth at the outset and in some detail the totality of the evidence relevant to sentencing that prompts us emphatically to reject this argument. The dissent criticizes this approach, maintaining that it unfairly reaches beyond “the offense of conviction,” which “amounts to a single act of attempted sexting.” Jacobs, C.J., Op. Dissenting (“Jacobs, C.J., Op.”), post at 298. This is wrong as a matter of law. While a district court cannot sentence a defendant to more severe punishment than that prescribed for the crimes of conviction, “[n]o limitation shall be placed on the information concerning the background, character, and conduct of a person convicted of an offense which a court of the United States may receive and consider for the purpose of imposing an appropriate sentence” within the prescribed range. 18 U.S.C. § 3661; see Williams v. New York, 337 U.S. 241, 247, 69 S.Ct. 1079, 93 L.Ed. 1337 (1949) (recognizing that sentencing judge is “not confined to the narrow issue of guilt” in determining punishment, but must act on “the fullest information possible concerning the defendant’s life and characteristics”); accord Pepper v. United States, — U.S. -, 131 S.Ct. 1229, 1240, 179 L.Ed.2d 196 (2011); Witte v. United States, 515 U.S. 389, 397-98, 115 S.Ct. 2199, 132 L.Ed.2d 351 (1995); Wisconsin v. Mitchell, 508 U.S. 476, 485, 113 S.Ct. 2194, 124 L.Ed.2d 436 (1993). Although the dissent cannot disavow this venerable — and codified — rule of sentencing law, see Jacobs, C.J., Op., post at 298, it can disregard it, justifying that action only with the conclusory plaint that we mischaracterize its views, see id. The dissent makes its views clear enough. It (1) minimizes evidence that Broxmeyer abused his position as a field hockey coach repeatedly to sexually abuse teenage girls; (2) criticizes the quality of that evidence while ignoring the fact that Broxmeyer carefully avoided an evidentiary hearing at which the details of events reported by the Probation Department in its Presentence Investigation Report (“PSR”), including multiple rapes, might be produced; (3) ignores Broxmeyer’s statements at sentencing, which showed no remorse and blamed his victims; and most troubling,'(4) proposes that sentencing judges wear blinders, confining the matters considered to the evidence supporting the crimes of conviction. We here emphasize that this view of sentencing has no place in our jurisprudence. The broad range of information that the district court was here entitled to consider in imposing sentence might usefully be thought to fall into three sets, each larger than the one before: (1) evidence establishing Broxmeyer’s guilt for the crimes of conviction, (2) evidence supporting particular Sentencing Guidelines enhancements, and (3) evidence properly informing the court’s exercise of its ultimate sentencing discretion under 18 U.S.C. § 3553(a). While the second set defeats Broxmeyer’s claim that procedural error in the application of the Guidelines renders his sentence unreasonable, it is the third, largest set that compels rejection of the claim that his sentence is substantively unreasonable. See generally United States v. Wernick, 691 F.3d 108, 117-18 (2d Cir.2012) (distinguishing between specified facts relevant to Guidelines application and broad range of information properly considered in district court’s determination of sentence under § 3553(a)). That evidence, developed at trial and reported in the PSR, which the district court adopted, showed that, at the time of his December 22, 2007 arrest, the then-37year-old Broxmeyer had worked for many years as a field hockey coach training female high school athletes in New York, New Jersey, and Pennsylvania. Broxmeyer’s interaction with the girls he coached frequently escalated from the athletic to the flirtatious to the overtly — and coarsely — sexual. For example, Broxmeyer sent several teenage girls an image of his erect penis, requesting that they provide him with sexually explicit images of themselves or others in return. He maintained such pictures in an electronic album and on two computers eventually seized pursuant to a warrant. Broxmeyer sometimes distributed these pictures to other teenagers to encourage them to produce similar images of themselves or other girls. Broxmeyer also engaged several teenage girls in a range of sexual conduct, including intercourse and sodomy. The sodomy, necessarily criminal because the girl involved was only 15, was proved to a jury’s satisfaction at Broxmeyer’s trial in this case. In addition, the adopted PSR recounts five rapes, two of them statutory, as well as other sexual. assaults on teenage girls. The district court properly considered Broxmeyer’s crimes of conviction in this context, see 18 U.S.C. §§ 3553(a)(1), 3661, and reasonably recognized that they could neither be dismissed as only “sexting,” see Jacobs, C.J., Op., post at 298, nor justified as “just joking around,” Resentencing Tr. at 19:4-5 (quoting defendant’s characterization of conduct). 1. Convicted Conduct a. Count Three: Attempted Production of Child Pornography Broxmeyer’s conviction for attempted production of child pornography was based on his November 2007 procurement of an image of 17-year-old K.T. posing suggestively in her underwear. K.T. testified that, while Broxmeyer served as her field hockey coach, he routinely sent her text messages in which he told her that she was beautiful and had a nice body, which made her feel special. In the course of their electronic communications, Broxmeyer sent K.T. a picture of his penis, and asked her to provide him with sexually explicit images of herself. In one communication admitted into evidence at trial, Broxmeyer told K.T. she could take such pictures in a bathroom using her cell phone, thereafter using the phone to transmit the images to him. K.T. eventually sent Broxmeyer the image of herself in her underwear. Because the image was suggestive, but not sexually explicit, Count Three charged Broxmeyer with attempted, rather than actual, production of child pornography. Upon receipt of the underwear picture, Broxmeyer praised KT.’s effort, but demanded more. When K.T. sent him other non-pornographic images, Broxmeyer rebuked her, stating, “you know that’s not what I was talking about.” Trial Tr. at 255:14-15. Eventually, in December 2007, K.T. sent Broxmeyer a pornographic picture in which she appeared nude, inserting a finger into her vagina. b. Count Five: Possession of Child Pornography KT.’s aforementioned pictures were among dozens of nude and semi-nude images of adolescent females found in Broxmeyer’s possession when law enforcement officers seized his online photo album and two personal computers. Among the images qualifying as child pornography were two depicting 17-year-old A.W., another field hockey player coached by Broxmeyer. In one, the girl is shown inserting a finger into her vagina; in the other she sprays water from a hand-held shower head toward her nude genital area. Broxmeyer had met A.W. in 2005 when, at age 15, she attended a field hockey camp at which he was coaching. Broxmeyer began flirting with the girl and, by 2007, had engaged her in sexual relations not only in New York, but also in California when he escorted the field hockey team on which A.W. played to a competition in that state. Broxmeyer and A.W. sometimes used cell phones to photograph themselves engaged in sexual acts. Broxmeyer also sent A.W. lewd and pornographic images of other teenage field hockey players, including the underwear and vagina images he had received from K.T. He challenged A.W. to obtain such images of other field hockey players for him, which A.W. did on several occasions. 2. Trial Evidence of Broxmeyer’s Criminal Sexual Assault of 15-Year-Old KM. In reversing Broxmeyer’s conviction on Count Four, this court identified no sufficiency problem in the evidence that Broxmeyer intended to — and did — engage a 15-year-old field hockey player, K.M., in criminal sexual activity, specifically, sodomy. The court concluded only that the evidence was insufficient to satisfy federal jurisdiction because the sodomy occurred before rather than after Broxmeyer took the girl across a state line. See United States v. Broxmeyer, 616 F.3d at 128-30; see also 18 U.S.C. § 2423(a). In these circumstances, although the proved sodomy could not qualify on remand as convicted conduct, it could still be considered in the district court’s Guidelines calculation and in its ultimate determination of sentence under § 3553(a). Accordingly, we summarize this evidence here. Beginning in September 2007, K.M.’s parents arranged for their daughter to travel on weekends from her home in Pennsylvania to New York or New Jersey to attend field hockey practices conducted by Broxmeyer. When, in early December 2007, a scheduling problem arose with respect to transporting K.M. home after a weekend practice in New York, Broxmeyer advised the girl’s parents that he himself would drive their daughter back to Pennsylvania. On December 9, 2007, at the outset of the return trip, Broxmeyer stopped in Johnson City, New York, at a community sports center that he managed called the Sportsplex and insisted that K.M. accompany him inside. There, Broxmeyer grabbed the girl, began kissing her, and removed his pants. Broxmeyer made K.M. sit in a chair, and holding the girl’s head in his hand, had her perform oral sex on him. Broxmeyer then drove K.M. home, admonishing her never to tell anyone what had happened, an instruction the girl followed until she heard of Broxmeyer’s arrest later in December, whereupon she told her parents of the sexual assault. Law enforcement authorities contacted K.M. and her family after learning of the assault from a New York field hockey player, J.B., in whom K.M. had confided. When investigators interviewed K.M., she revealed that her sexual assault had a familiar prelude: Broxmeyer had sent the girl a picture of his penis, solicited sexually explicit images of her in return, and engaged the girl in sexually explicit text messages, which in fact continued after the assault. 3. Broxmeyer’s Sexual Assaults on Other Teenagers The PSR detailed numerous other sexual assaults by Broxmeyer on teenage field hockey players. a. K.T. The PSR reported that K.T., the same 17-year-old whose transmittal of a suggestive underwear picture supported defendant’s Count Thi’ee conviction for attempted production of child pornography, see swpra Part I.A.l.a, claimed that Broxmeyer had raped her at the Sportsplex on the night of December 21, 2007. The girl reported the assault that same night when she went with her parents to a Binghamton hospital to seek treatment. There, she told police that, earlier that day, she had asked Broxmeyer to pick her and a friend up at a local mall. Broxmeyer took K.T. and her friend J.B., another 17-year-old field hockey player, to the Sportsplex, the site of the assault on KM. a few weeks earlier, claiming he had work to do there. Soon after their arrival, Broxmeyer started tickling K.T. and tried to remove her pants. K.T. protested that she was not consenting to any sexual activity and threatened to report Broxmeyer to the police. Broxmeyer persisted, ultimately penetrating KT.’s vagina with his penis. According to K.T., the assault ended when she bit Broxmeyer and kicked him in the groin. Nevertheless, KT. and her friend allowed Broxmeyer to take them home, and soon after, Broxmeyer sent KT. repeated apologetic text messages. When police questioned Broxmeyer in the early hours of the next morning, he admitted being at the Sportsplex the night before with KT. and J.B. and to tickling K.T. He denied ever having any sexual contact with K.T., or any other girls, although he admitted sending KT. nude pictures of himself and receiving pictures from her in return. In fact, Broxmeyer subsequently acknowledged other sexual activity with K.T., but maintained that it was consensual. That other activity, which K.T. had already disclosed in her December 22 police interview, occurred on December 7, 2007. K.T. told police that on that day Broxmeyer had invited her and J.B. to his apartment, purportedly to discuss college. There, Broxmeyer took K.T. into his bedroom, where, after kissing and fondling the girl, he took off his pants and had K.T. stimulate him with her hand until he ejaculated. b.J.B. On December 23, 2007, police questioned J.B., who corroborated elements of KT.’s account of the events of December 21, but stated that she had not seen the reported assault — purportedly because she had her eyes closed — although K.T. had told her of its occurrence. Nevertheless, J.B. advised police that she had herself been a victim of Broxmeyer’s assaults as had other teenage girls. Specifically, J.B. stated that sometime in November 2007, she had been at Broxmeyer’s apartment watching a movie with his girlfriend. While driving J.B. home, Broxmeyer stopped his car and started moving his hand up the girl’s leg, teasing her by saying “chicken.” The girl told him to stop and refused Broxmeyer’s instruction to undo her belt buckle. At that point, he drove her home. Although J.B. purported to be frightened by the November encounter, on December 1, 2007, she returned to Broxmeyer’s apartment to watch another movie, this time in the company of her 17-year-old friend J.C. During the movie, Broxmeyer led J.C. by the hand into his bedroom. J.C. emerged a short time later with a shocked look on her face, prompting J.B. to ask what had happened. Broxmeyer said he would show J.B., and proceeded to lead her into the bedroom, where he had forcible sexual intercourse with her. The next day, J.C. told J.B. that Broxmeyer had similarly assaulted her. Asked if she knew of any other minors whom Broxmeyer had sexually abused, J.B. identified K.M., a disclosure that, as noted earlier, led investigators to locate K.M. in Pennsylvania, resulting in her testifying against Broxmeyer at trial with respect to Count Four. c. J.C. Investigators also subsequently interviewed J.C., who confirmed being at Broxmeyer’s apartment with J.B. on December 1, 2007. She stated that, after Broxmeyer took her into a bedroom, he removed her pants and, over her protests, had sexual intercourse with her. He then instructed her not to tell anyone about what had occurred. d. M.G. Similarly, police interviewed M.G., a girl whom A.W. had identified as the person depicted in a suggestive photograph that Broxmeyer had shown her. M.G. testified at trial that Broxmeyer had been the coach of her club field hockey team for high-school age girls, during which time, he repeatedly flattered her appearance, sent her a photograph of his penis, and badgered her to send him “sexy” photographs of herself. Trial Tr. at 121:8. Eventually, M.G., who was 17 at the time, sent him a photograph of herself clad in underwear which Broxmeyer later showed to A.W. M.G. further testified that on one occasion when Broxmeyer had driven her home from a field hockey practice, he had stopped his car and sexually assaulted her by putting his finger inside her vagina. e. M.L. After Broxmeyer’s 2007 arrest, an adult woman identified in the PSR only as M.L. came forward and reported to investigators that some 15 years earlier, in 1991-92, when she was a 13-year-old field hockey player, defendant had subjected her to three escalating sexual assaults. On the first occasion, when the girl was in Broxmeyer’s car, he ran his hand up her thigh and said “chicken” before putting his hand into her pants and fondling her. On the second occasion, Broxmeyer forced the girl to perform oral sex on him. Finally, after a school dance in February 1992, Broxmeyer got the girl intoxicated and had sexual intercourse with her, after which he told her not to tell anyone as he could go to jail. B. Broxmeyer’s Sentencing 1. The PSR Guidelines Calculation and the Statutory Sentencing Ranges Broxmeyer’s Sentencing Guidelines calculation, as reported in the PSR, reflected a total offense level of 43 and a criminal history category of I, resulting in an advisory Guidelines sentence of life incarceration. Because life imprisonment exceeded the statutorily authorized maximum sentence of 40 years — which could be achieved by sentencing Broxmeyer to the maximum 30-year prison term for attempted production of child pornography, see 18 U.S.C. § 2251(e), and a consecutive maximum 10-year term for possession of child pornography, see id. § 2252A(b)(2) — the statutorily authorized maximum became the Guidelines sentence. See U.S.S.G. § 5Gl.l(a); United States v. Dorvee, 616 F.3d 174, 180-81 (2d Cir.2010). While the district court was not required to sentence Broxmeyer to a Guidelines sentence of 40 years’ incarceration, see United States v. Booker, 543 U.S. 220, 245, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), it could not sentence him to fewer than 15 years, the statutorily mandated minimum on the attempted production count of conviction, see 18 U.S.C. § 2251(e). 2. Broxmeyer’s Sentencing Submission On remand, Broxmeyer renewed objections to the PSR and to his Guidelines calculations that he had unsuccessfully-pursued at his initial sentencing. Broxmeyer generally disputed all PSR allegations of sexual assault, maintaining that he never forced himself on any of the accusing teenagers. He denied having any sexual relations with K.T., J.B., and J.C. on the occasions these girls accused him of rape, and he maintained that his conceded sexual relationship with 17-year-old A.W. was consensual, as was any sexual conduct he may have engaged in with 17-year-old K.T. on December 7, 2007, or with 15-year-old K.M. on December 9, 2007. To minimize further the seriousness of his conduct, Broxmeyer challenged the sexual explicitness of some of the photographs found in his possession, as well as the minority of some of the girls depicted therein. He also maintained that he did not send M.G. a photograph of his erect penis until she sent him a suggestive photograph of herself. He insisted that M.G.’s trial testimony — in response to a leading question — established only that Broxmeyer had “touched” her vagina, not that he had inserted his finger into it. Def.’s Resentencing Mem. at 9. Further, although M.G. testified that the action “shocked” her, Broxmeyer contended that this did not indicate that the contact was “unwelcome,” and he therefore objected to M.G. being considered a “victim.” Id. at 11. Broxmeyer also raised myriad challenges to the calculation of his Guidelines sentence, specifically to the enhancements for distributing child pornography, see U.S.S.G. § 2G2.1(b)(3); directing a minor to produce and distribute pornographic images of herself, see id. § 3B1.4; engaging in a pattern of child sex abuse or exploitation, see id. §§ 2G2.2(b)(5), 4B1.5(b)(l); using a computer to commit the possession crime, see id. § 2G2.2(b)(6); and possessing more than 10, but fewer than 150, images of child pornography, see id. § 2G2.2(b)(7)(A). 3. The District Court’s Sentencing Determination At Broxmeyer’s resentencing, the district court noted that it had already ruled on Broxmeyer’s objections to the PSR at the time of his original sentencing, and that nothing of significance had changed in the interim except for the reversal of convictions on Counts One, Two, and Four. Insofar as more victims had come forward in the interim, the district court assured Broxmeyer that it would not increase his sentence based on that new information. But insofar as Broxmeyer submitted that due process precluded the district court from relying on the untried allegations of sexual misconduct reported in the original PSR, the district court ruled to the contrary. “It’s a question of preponderance of the evidence and the court’s entitled to consider submissions made from anybody about conduct involved here and make a decision on how much it should consider to base its sentence on. Resentencing Tr. at 4:22-5:1. The district court nevertheless noted that if Broxmeyer “disagree[d] with that approach,” and wanted the court to go through all his objections again “step by step,” it was “glad to do it with [him].” Resentencing Tr. at 5:1-2. In response, defense counsel did not request any further rulings on factual objections to the assault evidence, much less a hearing. Counsel asked only that the court rule on objections to the PSR’s Sentencing Guidelines calculations. The district court summarily rejected all Guidelines objections and adopted the PSR’s calculations. Defense counsel proceeded to argue that sentencing factors specified in 18 U.S.C. § 3553(a), including the defendant’s character and history, warranted leniency and urged the court to impose a sentence of no more than the 15-year mandatory minimum. Before imposing sentence, the district court also heard from the prosecution and from Broxmeyer himself. After portraying himself as a person who was always “the first to step up and admit” any wrongdoing, Resentencing Tr. at 17:13-14, Broxmeyer proceeded to deny or minimize virtually all charges against him. He dismissed his sexual communications and pornographic picture exchanges with teenage students as “just joking around.” Id. at 19:4-5. He characterized those sexual relations he did acknowledge as “stupid,” id. at 19:7, and professed sorrow, not for the harm caused by his conduct, but for the fact “that it is blown up to this,” ie., his criminal prosecution, id. at 20:3-4. While indicating a willingness to “apologize to anybody if they were offended” by his conduct, id. at 20:4-5, Broxmeyer maintained that any hurt was “unintentional,” id. at 18:9. He insisted that he had never assaulted or raped anyone. Indeed, he suggested that he was not a victimizer but a victim of accusers who had been motivated to level false charges by Broxmeyer’s refusal to compromise his professional integrity to their advantage: I’ve irritated people in my professional life because of how I stood for certain things.... [TJhere are ... certain people that [the prosecutor] would like to say are victims that I wouldn’t kowtow to because I wouldn’t change the way I do business in order to make them look better and, in reality, what’s going on is certain people are using this to their advantage now. Id. at 19:13-23. Neither at trial nor sentencing did defendant proffer any support for this self-serving assertion. The district court proceeded to sentence Broxmeyer to concurrent prison terms of 30 years on Count Three and 10 years on Count Five. In explaining its decision to impose a sentence well above the mandatory 15-year minimum but below the 40-year statutory maximum recommended by the Guidelines, the district court acknowledged defendant’s preeminence in his field. See id. at 21:7-9 (“Colleges sought you, high schools sought you to be their coach. You’re good at what you did.”). Nevertheless, it found — with what can only be described as dignified understatement — that “for a long period of time,” Broxmeyer had “lost perspective,” failing to understand or not wanting to understand “what’s appropriate or not appropriate with young ladies.” Id. at 21:11-14. The district court explained that, even without regard to any sexual encounters, it viewed the text messaging and picture exchanges that informed the crimes of conviction as particularly serious, see id. at 21:20 (characterizing conduct as “way off the mark”), because, in fact, Broxmeyer was supposed to be the girls’ “mentor ... their guardian ... their instructor,” ie., the person who was “supposed to show them how to act,” id. at 21:16-18. As for Broxmeyer’s denials of any but consensual sexual encounters with teenage players, the district court apparently saw no need to explore the sordid particulars of each alleged encounter to find by a preponderanee that Broxmeyer had sexually assaulted teenagers in his care. It made this clear to Broxmeyer in rejecting his attempt to challenge these accusations by portraying himself as the victim of a vindictive conspiracy: [W]hen I take what you tell me as to what you didn’t do and what [defense counsel] tells me what you didn’t do and I contrast that to information I get from a number of sources that said you did do all of those things, how do you expect me to react to that? Do I have to conjure up in my mind some enormous conspiracy that all of these victims got together and said we’re going to get Broxmeyer for offending us? We’re going to tell all these lies about what he did to us sexually? Is that what I’m supposed to believe? Well, I don’t believe it for a minute.... Id. at 21:24-22:8. Concluding that it needed to impose a sentence that protected the public and provided general and specific deterrence, see 18 U.S.C. § 3553(a)(2)(B), (C), but nevertheless maintaining some hope for Broxmeyer’s eventual rehabilitation, the district court imposed the challenged 30-year sentence. II. Discussion In reviewing Broxmeyer’s sentencing challenges, our standard is “reasonableness,” “a particularly deferential form of abuse-of-discretion review” that we apply both to the procedures used to arrive at the sentence (procedural reasonableness) and to the length of the sentence (substantive reasonableness). United States v. Cavera, 550 F.3d 180, 188 & n. 5 (2d Cir.2008) (en banc). A. Procedural Reasonableness Broxmeyer submits that the district court committed procedural error in (1) failing to rule on his factual objections to the PSR and (2) miscalculating his Guidelines sentence. See id. at 190; see also United States v. Arevalo, 628 F.3d 93, 96 (2d Cir.2010). We are not persuaded. 1. Failure To Resolve Factual Disputes a. Waiver Broxmeyer contends that his sentence must be vacated and the case remanded for further proceedings because the district court failed to rule on each of his factual objections as required by Fed. R.Crim.P. 32(i)(3)(B). In fact, Broxmeyer waived any such argument before the district court. Although the district court noted that it had already ruled on Broxmeyer’s factual objections at the initial sentencing, it offered to do so again “step by step.” Resentencing Tr. at 5:2. Broxmeyer’s counsel did not accept this invitation, replying that defendant asked only that the court rule on his objections to the PSR’s Guidelines calculation. Indeed, after the district court made its Guidelines ruling and adopted the PSR, defense counsel stated, “Okay ... we can move forward with regard to sentencing.” Id. at 5:20-21. Counsel then proceeded to argue why the statutory sentencing factors set forth in 18 U.S.C. § 3553(a) supported a sentence at the mandatory minimum of 15 years’ imprisonment. This course of conduct is not surprising. A defendant may well try to minimize his guilt by raising objections to unfavorable information in a PSR, while still trying to avoid any appearance of a false denial that could result in his losing acceptance of responsibility consideration, receiving an enhancement for obstruction of justice, or otherwise aggravating his sentence. Those same concerns will often prompt him not to pursue a hearing or, as here, to decline a court’s offer of further factfinding. Indeed, one can well understand why Broxmeyer (and certainly his lawyer) would not have thought it in his interest to have the district court proceed “step by step” through the details of the many sexual assaults reported in the PSR, much less to have the district court hear each victim testify directly to those details. But having made the choice to forgo the district court’s offer of more specific findings on his objections, Broxmeyer will not be heard on appeal to complain of the inadequacy of the court’s factfinding. His actions demonstrate a true waiver of any such argument, precluding appellate review. See generally United States v. Quinones, 511 F.3d 289, 321 (2d Cir.2007) (discussing “true waiver”). b. Plain Error Even in the absence of true waiver, we would review the alleged Rule 32(i)(3)(B) failure only for plain error in light of Broxmeyer’s failure to voice any objection at resentencing. See United States v. Wagner-Dano, 679 F.3d 83, 90, 94 (2d Cir.2012) (adopting plain error review of Rule 32(i)(3)(B) claim where defendant failed to press factual objections not resolved by district court in adopting PSR); see also United States v. Marcus, — U.S. -, 130 S.Ct. 2159, 2164, 176 L.Ed.2d 1012 (2010) (observing that appellate court may correct forfeited error only where appellant demonstrates existence of (1) error, (2) that is “clear or obvious,” (3) that affects appellant’s substantial rights, and (4) that “seriously affeet[s] the fairness, integrity or public reputation of judicial proceedings” (internal quotation marks omitted)). Broxmeyer cannot show plain error here. While strict compliance with Rule 32 is clearly required by our precedent, see United States v. Arevalo, 628 F.3d at 96, Broxmeyer cites no case — nor are we aware of any — in which we have held that a district court, presented on remand with the same factual disputes on which it had already ruled at the initial sentencing, and with no appellate identification of error in those rulings, plainly fails in its Rule 32(i)(3)(B) obligations by expressly adopting those original rulings and not pronouncing them anew. See United States v. Wagner-Dano, 679 F.3d at 94 (observing that for an error to be “plain,” it “must be so obvious that the trial judge and prosecutor were derelict in countenancing it, even absent the defendant’s timely assistance in detecting it” (internal quotation marks omitted)). Thus, Broxmeyer certainly cannot demonstrate any error plainly established in existing law. Indeed, he cannot even show error. Insofar as Broxmeyer' objected to allegations that he had engaged teenage girls in non-consensual sexual activities, the district court did rule on this point at resentencing, telling Broxmeyer that as between the accusations put forward by “a number of sources” and defendant’s self-serving denials, the court rejected the latter because Broxmeyer’s insinuation of a wide-ranging conspiracy among his past and present field hockey players to accuse him falsely of sexual assaults was implausible. Resentencing Tr. at 22:1. If Broxmeyer did not think this statement, together with the district court’s earlier reference to its authority to “consider submissions made from anybody” if supported by a “preponderance of the evidence,” id. at 4:22-24, adequately addressed any concern he had about consideration of assault evidence, he was obliged to bring that to the district court’s attention, see United States v. Wagner-Dano, 679 F.3d at 92 (noting defendant’s obligation to object if he thinks district court has not addressed factual issue material to sentencing). Having failed to do so, he cannot demonstrate any procedural error by the district court. Insofar as Broxmeyer now faults the district court for considering untried assault accusations without affording him an opportunity to cross-examine his accusers, we observe that, although defendant’s re-sentencing memorandum noted that the disputed assault accusations had not been tested by cross-examination, Broxmeyer never actually sought a hearing for that purpose, nor did he argue that it would be procedural error to rely on the accusations in the absence of cross-examination. The omission appears to have been tactical rather than inadvertent. After all, when Broxmeyer was afforded an opportunity at trial to cross-examine two girls, K.M. and M.G., who testified to his assaults on them, he did so only minimally and to no apparent effect. Thus, the district court could reasonably have understood the cross-examination point raised at sentencing as urging that the accusations be accorded little weight rather than seeking a hearing. Even now, Broxmeyer does not point to any line of cross-examination that he might have pursued at a hearing to undermine his accusers’ credibility in a way that went beyond the arguments he presented to the district court. Thus, he also fails to demonstrate the substantial injury required for plain error. Further, Broxmeyer cannot demonstrate that the district court’s failure to hold a hearing sua sponte was itself plain error. See United States v. Verkhoglyad, 516 F.3d 122, 128 (2d Cir.2008) (observing that forfeited claims of procedural error are reviewed only for plain error). A sentencing court’s “largely unlimited” discretion to review information relevant to the defendant and his crime permits it to consider hearsay evidence. United States v. Gomez, 580 F.3d 94, 105 (2d Cir.2009) (internal quotation marks omitted); see also 18 U.S.C. § 3661. Moreover, it is well established that a district court need not hold an evidentiary hearing to resolve sentencing disputes, as long as the defendant is 'afforded “some opportunity to rebut the Government’s allegations.” United States v. Phillips, 431 F.3d 86, 93 (2d Cir.2005) (internal quotation marks omitted). Here, Broxmeyer was afforded that rebuttal opportunity through written submissions and arguments advanced by counsel in connection with both sentencings and through Broxmeyer’s own statement at his resentencing. On this record, we identify no plain procedural error in the district court’s fact-finding. 2. Guidelines Calculations In considering Broxmeyer’s challenge to the calculation of his Guidelines sentence, we review the district court’s interpretation of the Guidelines de novo, and its findings of fact relevant to the Guidelines application for clear error. See United States v. Richardson, 521 F.3d 149, 156 (2d Cir.2008). a. Count Three: Attempted Production of Child Pornography Broxmeyer argues that the district court miscalculated his Guidelines for attempted production of child pornography in applying enhancements for use of a minor, see U.S.S.G. § 3B1.4, and distribution, see id. at § 2G2.1(b)(3). Both arguments are meritless. (1) Use of a Minor Enhancement Section 3B1.4 of the Guidelines provides for the base offense level of any crime to be enhanced by two if the defendant “used or attempted to use a person less than eighteen years of age to commit the offense.” U.S.S.G. § 3B1.4. The enhancement does not apply, however, if the offense guideline for the crime of conviction already “incorporates this factor.” See U.S.S.G. § 3B1.4 cmt. n.2. Relying on this comment, Broxmeyer argues that because production (or attempted production) of child pornography necessarily involves the use of a minor, no § 3B1.4 enhancement was warranted in his case. Broxmeyer’s argument fads because it conflates engaging (or attempting to engage) a minor in “sexually explicit conduct for the purpose of producing any visual depiction of such conduct,” 18 U.S.C. § 2251(a), the proscribed use at issue in his crime of conviction, with using a minor to photograph that conduct in an attempt to produce child pornography. In this case, Broxmeyer used 17-year-old K.T. both as the model and the photographer in his attempt to produce child pornography. The base offense level of 32, however, was dictated only by K.T.’s participation in the former role. Indeed, that base offense level would have applied even if someone else, including an adult, had been the photographer. But if the other person acting as photographer had been another child, a § 3B1.4 enhancement would properly apply in recognition of that distinct harm. The same conclusion applies here, where a defendant visits these distinct harms on the same minor. See United States v. Sabhnani, 599 F.3d 215, 251 (2d Cir.2010) (holding no impermissible duplication from application of multiple Guidelines adjustments that “aim at different harms emanating from the same conduct” (internal quotation marks omitted)). Thus, we conclude that there was no procedural error in the district court’s application of a § 3B1.4 enhancement to the calculation of Broxmeyer’s Guidelines offense level. (2) Distribution Enhancement Section 2G2.1(b)(3) of the Guidelines provides for a two-level enhancement to the base offense level of 32 for production (or attempted production) of child pornography if “the offense involved distribution.” The district court determined that such an enhancement was warranted here by both KT.’s distribution of images of herself to Broxmeyer and Broxmeyer’s redistribution of those images to A.W. Broxmeyer argues that the enhancement was unwarranted because KT.’s distribution of images to him was implicit in the crime of conviction and Broxmeyer’s redistribution of the images to A.W. was not “relevant conduct.” We need only discuss Broxmeyer’s redistribution to reject these arguments as meritless. Critical to that discussion is a legal principle stubbornly ignored by both Broxmeyer and the dissent: under the Sentencing Guidelines, an “offense” includes not only the specific conduct satisfying the elements of the crime of conviction, but all conduct “relevant” to the crime as detailed in § 1B1.3. See U.S.S.G. § 1B1.1 cmt. n.l(H); see also id. § 1B1.3 cmt. n.l (observing that “principles and limits of sentencing accountability under the guideline are not always the same as the principles and limits of criminal liability”). The Guidelines define relevant conduct to include, among other things, “all acts and omissions committed, aided, abetted, counseled, commanded, induced, procured, or willfully caused by the defendant ... that occurred during the commission of the offense of conviction,” U.S.S.G. § lB1.3(a)(l)(A), as well as “all harm that resulted from [such] acts and omissions, ... and all harm that was the object of such acts and omissions,” id. § lB1.3(a)(3). Here, the record evidence demonstrates that the object of the attempted crime of conviction was to induce a minor to produce sexually explicit images of herself. In this context, Broxmeyer’s procurement of a sexually suggestive, albeit not sexually explicit, image of K.T. sufficed to prove him guilty of attempt. See generally United States v. Farhane, 634 F.3d 127, 145 (2d Cir.2011) (observing that conviction for attempt requires proof that defendant (a) had intent to commit object crime and (b) engaged in conduct amounting to substantial step towards commission). But Broxmeyer’s attempt to achieve his criminal objective hardly concluded with that procurement. After receiving the suggestive image of K.T. in her underwear, Broxmeyer continued to cajole and badger the girl for a sexually explicit photograph of herself, ultimately receiving the image of K.T. inserting a finger into her vagina. The harm resulting from inducing a minor’s production and transmittal of such a sexually explicit image of herself is distinct from and greater than the harm reflected in the production and transmittal of the suggestive underwear image. Moreover, the production of a sexually explicit image was the real object of the attempt crime of conviction and, therefore, properly treated as relevant conduct for purposes of determining Broxmeyer’s offense level. Further, the record shows that, in attempting to have K.T. produce sexually explicit images of herself, Broxmeyer’s object was not limited to his own possession and viewing of that pornography. He further sought to distribute the images to other minors in order to induce the production of still more child pornography. As the Supreme Court has recognized, distribution of child pornography subjects the depicted child to more harm than that caused by production alone. See generally New York v. Ferber, 458 U.S. 747, 759, 102 S.Ct. 3348, 73 L.Ed.2d 1113 (1982) (observing, in context of First Amendment challenge to state law punishing dissemination of child pornography, that pornographic materials “are a permanent record of the children’s participation and the harm to the child is exacerbated by their circulation”). Thus, redistribution of both images of K.T. to A.W. is properly viewed as a further harmful object of, and relevant conduct to, the attempted production crime of conviction. As such, the district court correctly applied the two-level enhancement for distribution called for by U.S.S.G. § 2G2.1(b)(3). b. Adjustments to the Combined Offense Level (1) Acceptance of Responsibility Broxmeyer contends that the district court erroneously denied him the two-level downward adjustment to his combined offense level available to a defendant who “clearly demonstrates acceptance of responsibility for his offense.” U.S.S.G. § 3El.l(a). Whether a defendant has carried his burden to demonstrate acceptance of responsibility is “a factual question” on which we defer to the district court unless its refusal to accord such consideration is “without foundation.” United States v. Taylor, 475 F.3d 65, 68 (2d Cir.2007) (internal quotation marks omitted). Here, the record shows that the district court’s denial of § 3E1.1 consideration rests on a solid foundation. As the commentary to § 3E1.1 makes plain, the adjustment is generally not available to a defendant such as Broxmeyer “who put[ ] the government to its burden of proof at trial by denying the essential factual elements of guilt,” even if, after conviction, he admits guilt and expresses remorse. U.S.S.G. § 3El.l(a) cmt. n.2. To be sure, the adjustment can apply in “rare situations” to a defendant who goes to trial to assert and preserve issues that do not relate to factual guilt where pre-trial statements and conduct evidence acceptance. Id. But that is not this case. Neither before nor after trial did Broxmeyer ever clearly accept responsibility for attempting to produce and possess child pornography. Rather, he repeatedly sought to minimize his culpability for these crimes by suggesting that his sexual text messaging and photo exchanges only mimicked practices already prevalent among teenagers. Further, he stated that his own conduct had been “blown up” out of proportion in being made the subject of a criminal prosecution. Resentencing Tr. at 20:3. On this record, we easily defer to the district court’s decision not to accord consideration for acceptance of responsibility. (2) Pattern of Activity Broxmeyer faults the district court’s application of a five-level enhancement to his combined offense level pursuant to U.S.S.G. § 4B1.5(b)(l), arguing that the record fails to show the “pattern of activity involving prohibited sexual conduct” with a minor required by that guideline. While the government maintains that there is a “plethora of evidence indicating Broxmeyer engaged” in prohibited sexual conduct with minors, Appellee’s Br. at 49, we need identify only two such occasions to uphold the district court’s pattern finding, see U.S.S.G. § 4B1.5(b)(l) & cmt. n.4(B)(i) (stating that “defendant engaged in a pattern of activity involving prohibited sexual conduct if on at least two separate occasions, the defendant engaged in prohibited sexual conduct with a minor”). In doing so, we are mindful that the district court was entitled to consider any prohibited sexual conduct Broxmeyer engaged in with a minor, “without regard to whether the occasion (I) occurred during the course of the instant offense; or (II) resulted in a conviction for the conduct that occurred on that occasion.” Id. § 4B1.5 cmt. n.4(B)(ii); see, e.g., United States v. Phillips, 431 F.3d at 90 (holding that un-adjudicated act of sex abuse committed when defendant was a juvenile qualified as occasion of prohibited sexual conduct under § 4B1.5(b)). “Prohibited sexual conduct” includes not only conduct violating specified federal criminal statutes, id. § 4B1.5 cmt. n.4(A)(i) (citing 18 U.S.C. § 2426(b)(1)(A) (specifying federal offenses listed under chapters 109A, 110, 117, or section 1591 of title 18 of the United States Code)), but also conduct violating state law that would have constituted one of these specified federal offenses “if the conduct had occurred within the special maritime and territorial jurisdiction of the United States,” 18 U.S.C. § 2426(b)(1)(B). Broxmeyer’s conviction on Count Three clearly provides one of the two occasions of prohibited sexual conduct necessary to establish a pattern of activity. Attempted production of child pornography in violation of 18 U.S.C. § 2251(a) and (e) is a federal crime codified in chapter 110 of title 18 of the United States Code. See 18 U.S.C. § 2426(b)(1)(A). The dissent contends that the crime of conviction should not be counted as one occasion of prohibited sexual conduct in identifying a pattern. See Jacobs, C.J., Op., post at 301-02 & n. 6. The dissent cites no authority for this argument, which we reject. If the dissent were correct, one would expect the Guidelines commentary to state that “defendant engaged in a pattern of activity involving prohibited sexual conduct if on at least two separate occasions in addition to the crime of conviction, the defendant engaged in prohibited sexual conduct with a minor.” In the absence of any such qualifier, we decline to construe § 4B 1.5(b)(1) as the dissent proposes. Instead, we accord Guidelines language its plain meaning: “two” means two, not three; and “separate” means the two occasions must be separate from each other, not that the two occasions demonstrating a pattern must be separate from (and in addition to) the crime of conviction. See generally United States v. Phillips, 431 F.3d at 92 (construing Guidelines “as if they were a statute, giving the words used their common meaning, absent a clearly expressed manifestation of contrary intent” (internal quotation marks omitted)). We further note that this guideline is intended to identify “repeat sex offenders,” who pose “a continuing danger to the public.” See U.S.S.G. § 4B1.5 cmt. background. In other contexts — specifically, racketeering — the law recognizes that two crimes can suffice to demonstrate a pattern of conduct posing a continuing danger to the public, even when the burden of proof is beyond a reasonable doubt. See United States v. Eppolito, 543 F.3d 25, 50 (2d Cir.2008). We reach the same conclusion here. Proof of any two separate occasions of prohibited sexual conduct—one of which can be the crime of conviction-permits the district court to find that a defendant poses the sort of continuing danger supporting a § 4B 1.5(b) enhancement. A second occasion of prohibited sexual conduct is Broxmeyer’s engagement of 15-year-old KM. in sodomy. Indeed, because this sodomy was preceded by Broxmeyer’s efforts to persuade KM. to produce pornographic images of herself, just as Broxmeyer’s sexual assault on K.T. followed his efforts to have her produce pornographic images of herself, there was particular reason to view the sodomy and the production crime of conviction as indicative of a pattern of prohibited sexual conduct. Our dissenting colleague nevertheless labels Broxmeyer’s engagement of KM. in sodomy as a “dubious” predicate for identifying a § 4B1.5(b)(l) pattern, emphasizing that this court reversed Broxmeyer’s 18 U.S.C. § 2423(a) conviction for this conduct. Jacobs, C.J., Op., post at 302. But reversal of a conviction does not preclude conduct from informing sentence. Cf. United States v. Vaughn, 430 F.3d 518, 527 (2d Cir.2005) (reiterating that even acquitted conduct can be used to calculate Guidelines sentencing range if proved by preponderance). That conclusion applies with particular force here because, as we have already observed, the cited reversal was based only on a failure to establish federal jurisdiction. This court did not identify any sufficiency defect in the trial proof of the, sodomy itself, nor could it have in light of KM.’s direct testimony. Because this proved sodomy plainly violated N.Y. Penal Law § 130.40(2) (prohibiting persons aged 21 and older from engaging in oral sex with person under age of 17), and would have violated 18 U.S.C. § 2243(a), one of the crimes referenced in § 2426(b)(1)(A), if committed within the special maritime or territorial jurisdiction of the United States, it undoubtedly qualifies as a predicate for purposes of the Guidelines pattern enhancement, see id. § 2426(b)(1)(B). Unable to challenge this conclusion as a matter of law, the dissent suggests that the sodomy should not be relied on here because it “did not occur” to the district court to consider Broxmeyer’s assault on KM. under that part of § 2426(b)(1)(B) referring to “state offenses that would be federal offenses if done on the high seas or in a post office.” Jacobs, C.J., Op., post at 302. This pronouncement is pure speculation and necessarily defeated by “the presumption that the district court knew and applied the law correctly.” United States v. Fernandez, 443 F.3d 19, 30 (2d Cir.2006) (internal quotation marks omitted). In any event, we may affirm a Guidelines enhancement “on any basis for which there is a record sufficient to permit conclusions of law, including grounds upon which the district court did not rely.” United States v. Palmer, 68 F.3d 52, 56 (2d Cir.1995) (internal quotation marks omitted). For reasons already stated, we easily conclude that the sodomy evidence pertaining to KM. qualifies as a matter of law as a U.S.S.G. § 4B1.5(b)(l) predicate pursuant to 18 U.S.C. § 2426(b)(1)(B). Nor does the district court’s sentencing reference to Broxmeyer’s “extensive history of sexually abusing children,” Resentencing Tr. at 24:4, support the dissent’s conclusion that only “untried offenses,” and not KM.’s sodomy, informed the district court’s pattern determination. Jacobs, C.J., Op., post at 302. First, the statement was made long after the district court had calculated Broxmeyer’s Guidelines sentence. See Re-sentencing Tr. at 21:12-14. Thus, it cannot properly be read to explain the district court’s application of a § 4B1.5(b)(l) Guidelines enhancement. Rather, the statement was made to explain the court’s exercise of its broad sentencing discretion pursuant to 18 U.S.C. § 3553(a). In exercising that discretion, the district court was not limited to conduct that could support a § 4B1.5(b)(l) enhancement; it was entitled to consider any “information concerning the background, character, and conduct” of the defendant, including the totality of record evidence pertaining to his exploitation of teenage girls under his care. 18 U.S.C. § 3661; see United States v. Cavera, 550 F.3d at 190-91; see also United States v. Wernick, 691 F.3d at 117—18 (recognizing district court’s discretion to consider “broad range of information” in evaluating § 3553(a) sentencing factors, even if not relevant to Guidelines calculation). Second, when the district court referenced Broxmeyer’s “extensive history of sexually abusing children” as among the factors considered in determining Broxmeyer’s sentence, Resentencing Tr. at 24:4, we do not understand it to have been referencing only the evidence of sexual assaults, much less only the evidence of untried sexual assaults. Rather, we understand the district court to have used the word “abuse” in its broadest sense to reach, in addition, the extensive evidence, much of it adduced at trial, of Broxmeyer encouraging teenagers he was supposed to mentor to engage with him in sexually suggestive communications and to create and transmit pornographic images of themselves and others. Third, and more to the point, the suggestion that the district court did not include Broxmeyer’s engagement of K.M. in sodomy in its reference to defendant’s “extensive history of sexually abusing children” — or in its earlier Guidelines pattern determination — is not only speculative, but also implausible. The district court heard K.M. testify at trial to how, after her parents arranged for Broxmeyer to coach her in field hockey, he pestered the 15-year-old with sexually explicit text messages, sent her images of his penis, solicited sexually explicit photographs in return, and ultimately engaged her in sodomy. It knew, moreover, that as to this 15-year-old there was no question as to consent. Further, KM.’s father appeared at Broxmeyer’s initial sentencing to advise the district court as to the effect of defendant’s abuse on his daughter and his family. In these circumstances, there is no possibility of the district court overlooking Broxmeyer’s abuse of K.M. or not including it within it reference to his “extensive history of sexually abusing children.” Thus, without regard to the other prohibited sexual conduct found by the district court, the production crime of conviction and the engagement of K.M. in sodomy — both proved at trial — are sufficient by themselves to support the district court’s application of a U.S.S.G. § 4B1.5(b)(l) pattern enhancement to the calculation of Broxmeyer’s Guidelines sentence. c. Count Five Objections Insofar as Broxmeyer argues that the district court committed procedural error in calculating his adjusted offense level with respect to Count Five, we need not address his arguments because any error would necessarily be harmless. Under the Guidelines’ grouping rules, the district court’s calculation of an adjusted offense level of 32 for Broxmeyer’s possession of child pornography contributed only a one-level enhancement to his total offense level for both crimes of conviction. See U.S.S.G. § 3D1.4(b). But because Broxmeyer’s resulting total offense level of 44 exceeded the highest offense level listed in the Sentencing Table, the district court treated Broxmeyer’s offense level as 43, see U.S.S.G. Ch. 5, Pt. A, cmt. n. 2, effectively negating the impact of the one-level grouping enhancement resulting from the Count Five offense-level calculation. In these circumstances, any error in the Count Five calculation would necessarily be harmless because it “would not, by itself, have made any difference” to the calculation of Broxmeyer’s sentencing range. United States v. Hertular, 562 F.3d 433, 448 (2d Cir.2009). In sum, we identify no procedural error that renders Broxmeyer’s sentence unreasonable so as to warrant remand. B. Substantive Reasonableness Broxmeyer submits that his 30-year prison sentence should be vacated as substantively unreasonable. In making this argument, he bears a heavy burden because our review of a sentence for substantive reasonableness is particularly deferential. See Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007) (instructing appellate courts to give “due deference” to district court sentencing decisions, taking into account totality of circumstances); United States v. Rigas, 583 F.3d 108, 123 (2d Cir.2009) (analogizing substantive unreasonableness review to manifest-injustice and shocks-the-conscience standards). That deference derives from a respect for the distinct institutional advantages that district courts enjoy over their appellate counterparts in making an “individualized assessment” of sentence under 18 U.S.C. § 3553(a). Gall v. United States, 552 U.S. at 50, 51-52, 128 S.Ct. 586; accord United States v. Jones, 531 F.3d 163, 170 (2d Cir.2008). Among those advantages is a district court’s unique factfinding position, which allows it to hear evidence, make credibility determinations, and interact directly with the defendant (and, often, with his victims), thereby gaining insights not always conveyed by a cold record. See Gall v. United States, 552 U.S. at 51-52, 128 S.Ct. 586; United States v. Jones, 531 F.3d at 171. Thus, while appellate courts have a role to play in “patrol[ling] the boundaries of reasonableness,” United States v. Cavera, 550 F.3d at 191, we do so modestly, not substituting our own judgment for that of district courts, see id. at 189, but rather, identifying as substantively unreasonable only those sentences that are so “shockingly high, shockingly low, or otherwise unsupportable as a matter of law” that allowing them to stand would “damage the administration of justice,” United States v. Rigas, 583 F.3d at 123. This is not such a case. In urging us to conclude otherwise, Broxmeyer argues that the district court assigned undue weight to untested aggravating allegations of sexual misconduct while failing to give sufficient weight to mitigating factors. He maintains, and our dissenting colleague agrees, that, if the district court had properly weighed the totality of the circumstances, the only substantively reasonable sentence it could have imposed would have been the statutory minimum prison term of 15 years. Wé are not persuaded. The particular weight to be afforded aggravating and mitigating factors “is a matter firmly committed to the discretion of the sentencing judge,” United States v. Fernandez, 443 F.3d at 32, with appellate courts seeking to ensure only that a factor “can bear the weight assigned it under the totality of circumstances in the case,” United States v. Cavera, 550 F.3d at 191. In making that determination, we are mindful that “facts may frequently point in different directions so that even experienced district judges may reasonably differ, not only in their findings of fact, but in the relative weight they accord competing circumstances.” United States v. Jones, 531 F.3d at 174. Applying these principles here, we begin by noting that 15 years is the congressionally' identified minimum pris