COOK, Circuit Judge.
Following a two-day trial, a jury found Eddie Allen Jackson guilty of three counts of child sex trafficking. He appeals, arguing that the district court improperly excluded evidence of the minor victims’ prostitution histories and that his 360-month sentence is procedurally and substantively unreasonable. Finding no error, we AFFIRM.
I.
In 2012, Jackson repeatedly drove sixteen-year-old Adrianna, fourteen-year-old Alissa, and fifteen-year-old Alexandra, from Muskegon to Grand Rapids, Michigan. Jackson plied them with flavored vodka, cigarettes, and marijuana. For the victims, this eased what came next: walking up and down Division Street, a known prostitution area, to solicit men for sex.
Jackson controlled all facets of the prostitution trips. He provided transportation and condoms. He determined where the teenagers would have sex for money — on Division Street, at a nearby America’s Best Inn, or at the so-called “Mexican house.” And he set the transaction terms, demanding that the victims collect extra money from customers who took longer than fifteen minutes. In return, the victims received 50% of the prostitution money, as well as gifts of clothes and tattoos. [462]*462But they feared Jackson, who hit Alissa and threatened to shoot Adrianna.
In December 2013, a grand jury indicted Jackson on three counts of child sex trafficking in violation of 18 U.S.C. §§ 1591(a)(1), (b)(2). Before trial, Jackson noticed his intent to present evidence that the minor victims prostituted for other pimps. After a hearing, the court excluded the evidence under • Federal Rule of Evidence 412, finding that the rule’s exceptions did not apply and that the evidence would “likely introduce prejudice and confusion into the trial.”
At trial the victims testified about their prostitution, their relationships with Jackson, and their initial reluctance to cooperate with prosecutors. Also testifying was FBI Special Agent James Hardie, who described typical relationships between pimps and vulnerable victims like Adrianna, Alissa, and Alexandra. In particular, Agent Hardie noted that minor victims often refuse at first to cooperate in sex-trafficking prosecutions out of loyalty to their pimps
The jury convicted Jackson on all three counts. In the ensuing weeks, Jackson twice contacted Adrianna and her family. The government moved for an emergency protective order, which was granted. The court enjoined Jackson from harassing or otherwise contacting Adrianna, Alissa, or Alexandra for three years. The court then sentenced Jackson to 360 months of imprisonment on each count of sex trafficking, to run concurrently. Jackson timely appealed his conviction and sentence.
II.
First, Jackson contends that the district court erred in excluding evidence that the victims prostituted themselves for other pimps. We review for abuse of discretion. United States v. Willoughby, 742 F.3d 229, 234 (6th Cir.2014).
Although Federal Rule of Evidence 412 prohibits “evidence offered to prove that a victim engaged in other sexual behavior,” Jackson maintains that the victims’ prostitution histories fall within one of the rule’s exceptions — “evidence whose exclusion would violate [his] constitutional rights.” Fed.R.Evid. 412(a)(1), (b)(1)(C). Banning evidence of the victims’ other pimps, Jackson argues, denied him his Sixth Amendment right to confront the prosecution’s witnesses through cross-examination, as well as his right to present a complete defense. See Jordan v. Warden, Lebanon Corr. Inst., 675 F.3d 586, 593 (6th Cir.2012).
The Sixth Amendment does not safeguard all avenues of cross-examination. Boggs v. Collins, 226 F.3d 728, 736 (6th Cir.2000); see also United States v. Anderson, 139 F.3d 291, 303 (1st Cir.1998) (using prior commercial sex acts to impeach the victim’s credibility “embodies] a particularly offensive form of stereotyping” and is not permissible). But it does protect Jackson’s right to expose through cross-examination a witness’s “motivation in testifying” or, more specifically, a “prototypical form of bias.” Boggs, 226 F.3d at 737. Jackson insists that each victim’s prostitution history reveals her motive to tag Jackson as her pimp to avoid prosecution herself or to shield the true pimp from prosecution.
If the court curtails cross-examination of a witness on motivation or bias, we ask whether the jury could assess those through other evidence. Boggs, 226 F.3d at 739, And if not, we balance thé Sixth Amendment violation against the government’s interest in excluding the testimony. Id.
Here, the jury heard testimony about the victims’ motives to name Jackson as their pimp. Adrianna admitted that [463]*463the government agreed not to prosecute her for prostitution if she testified against Jackson. So too Alissa, for whom the government dropped prostitution charges. And here, the government’s interest in exclusion outweighed any Sixth Amendment violation. Jackson’s proposed line of cross-examination strayed from any usual form of bias. His planned cross-examination required the jury to infer or speculate that the girls initially denied but later admitted to prostituting for Jackson in a calculated scheme to protect other pimps. As the district court recognized, this “is not a natural inference and appears to be based on little more than speculation.” Instead, the prototypical loyalty that prostitutes show to their pimps explains each victim’s about-face on prostituting for Jackson. Given the tenuous inferences needed to connect the prostitution evidence to bias against Jackson, any Sixth Amendment interest was negligible. In contrast, the government’s interest in excluding the evidence under the rape-shield law abounded, particularly because the victims were minors. See United States v. Ogden, 685 F.3d 600, 606 (6th Cir.2012) (finding Rule 412’s protections “especially important” for underage victims).
Nor did the court deny Jackson the opportunity to present a complete defense. The excluded evidence addressed no element of the offense and had little bearing on Jackson’s guilt, while the government had a strong interest in excluding it. See Ogden, 685 F.3d at 605-06 (finding that Ogden presented a complete defense to child pornography charges without introducing the minor victim’s sexually explicit chat logs).
The district court acted within its discretion in excluding evidence of the victims’ prostitution histories.
III.
Second, Jackson challenges the procedural and substantive reasonableness of his 360-month sentence.
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COOK, Circuit Judge.
Following a two-day trial, a jury found Eddie Allen Jackson guilty of three counts of child sex trafficking. He appeals, arguing that the district court improperly excluded evidence of the minor victims’ prostitution histories and that his 360-month sentence is procedurally and substantively unreasonable. Finding no error, we AFFIRM.
I.
In 2012, Jackson repeatedly drove sixteen-year-old Adrianna, fourteen-year-old Alissa, and fifteen-year-old Alexandra, from Muskegon to Grand Rapids, Michigan. Jackson plied them with flavored vodka, cigarettes, and marijuana. For the victims, this eased what came next: walking up and down Division Street, a known prostitution area, to solicit men for sex.
Jackson controlled all facets of the prostitution trips. He provided transportation and condoms. He determined where the teenagers would have sex for money — on Division Street, at a nearby America’s Best Inn, or at the so-called “Mexican house.” And he set the transaction terms, demanding that the victims collect extra money from customers who took longer than fifteen minutes. In return, the victims received 50% of the prostitution money, as well as gifts of clothes and tattoos. [462]*462But they feared Jackson, who hit Alissa and threatened to shoot Adrianna.
In December 2013, a grand jury indicted Jackson on three counts of child sex trafficking in violation of 18 U.S.C. §§ 1591(a)(1), (b)(2). Before trial, Jackson noticed his intent to present evidence that the minor victims prostituted for other pimps. After a hearing, the court excluded the evidence under • Federal Rule of Evidence 412, finding that the rule’s exceptions did not apply and that the evidence would “likely introduce prejudice and confusion into the trial.”
At trial the victims testified about their prostitution, their relationships with Jackson, and their initial reluctance to cooperate with prosecutors. Also testifying was FBI Special Agent James Hardie, who described typical relationships between pimps and vulnerable victims like Adrianna, Alissa, and Alexandra. In particular, Agent Hardie noted that minor victims often refuse at first to cooperate in sex-trafficking prosecutions out of loyalty to their pimps
The jury convicted Jackson on all three counts. In the ensuing weeks, Jackson twice contacted Adrianna and her family. The government moved for an emergency protective order, which was granted. The court enjoined Jackson from harassing or otherwise contacting Adrianna, Alissa, or Alexandra for three years. The court then sentenced Jackson to 360 months of imprisonment on each count of sex trafficking, to run concurrently. Jackson timely appealed his conviction and sentence.
II.
First, Jackson contends that the district court erred in excluding evidence that the victims prostituted themselves for other pimps. We review for abuse of discretion. United States v. Willoughby, 742 F.3d 229, 234 (6th Cir.2014).
Although Federal Rule of Evidence 412 prohibits “evidence offered to prove that a victim engaged in other sexual behavior,” Jackson maintains that the victims’ prostitution histories fall within one of the rule’s exceptions — “evidence whose exclusion would violate [his] constitutional rights.” Fed.R.Evid. 412(a)(1), (b)(1)(C). Banning evidence of the victims’ other pimps, Jackson argues, denied him his Sixth Amendment right to confront the prosecution’s witnesses through cross-examination, as well as his right to present a complete defense. See Jordan v. Warden, Lebanon Corr. Inst., 675 F.3d 586, 593 (6th Cir.2012).
The Sixth Amendment does not safeguard all avenues of cross-examination. Boggs v. Collins, 226 F.3d 728, 736 (6th Cir.2000); see also United States v. Anderson, 139 F.3d 291, 303 (1st Cir.1998) (using prior commercial sex acts to impeach the victim’s credibility “embodies] a particularly offensive form of stereotyping” and is not permissible). But it does protect Jackson’s right to expose through cross-examination a witness’s “motivation in testifying” or, more specifically, a “prototypical form of bias.” Boggs, 226 F.3d at 737. Jackson insists that each victim’s prostitution history reveals her motive to tag Jackson as her pimp to avoid prosecution herself or to shield the true pimp from prosecution.
If the court curtails cross-examination of a witness on motivation or bias, we ask whether the jury could assess those through other evidence. Boggs, 226 F.3d at 739, And if not, we balance thé Sixth Amendment violation against the government’s interest in excluding the testimony. Id.
Here, the jury heard testimony about the victims’ motives to name Jackson as their pimp. Adrianna admitted that [463]*463the government agreed not to prosecute her for prostitution if she testified against Jackson. So too Alissa, for whom the government dropped prostitution charges. And here, the government’s interest in exclusion outweighed any Sixth Amendment violation. Jackson’s proposed line of cross-examination strayed from any usual form of bias. His planned cross-examination required the jury to infer or speculate that the girls initially denied but later admitted to prostituting for Jackson in a calculated scheme to protect other pimps. As the district court recognized, this “is not a natural inference and appears to be based on little more than speculation.” Instead, the prototypical loyalty that prostitutes show to their pimps explains each victim’s about-face on prostituting for Jackson. Given the tenuous inferences needed to connect the prostitution evidence to bias against Jackson, any Sixth Amendment interest was negligible. In contrast, the government’s interest in excluding the evidence under the rape-shield law abounded, particularly because the victims were minors. See United States v. Ogden, 685 F.3d 600, 606 (6th Cir.2012) (finding Rule 412’s protections “especially important” for underage victims).
Nor did the court deny Jackson the opportunity to present a complete defense. The excluded evidence addressed no element of the offense and had little bearing on Jackson’s guilt, while the government had a strong interest in excluding it. See Ogden, 685 F.3d at 605-06 (finding that Ogden presented a complete defense to child pornography charges without introducing the minor victim’s sexually explicit chat logs).
The district court acted within its discretion in excluding evidence of the victims’ prostitution histories.
III.
Second, Jackson challenges the procedural and substantive reasonableness of his 360-month sentence. According to Jackson, the district court erroneously imposed an obstruction-of-justice enhancement, miscalculated his criminal-history score, and neglected to explain why it overruled his objections to two other enhancements.
A. Obstruction-of-Justice Enhancement
After the trial but before sentencing, Jackson mailed Adrianna a letter asking her “[h]ow could [she] get on the stand and lie after lie,” and telling her to “think of what [she] ha[s] done.” Jackson also contacted Adrianna’s mother by phone. The court interpreted these communications as efforts “to get to - these girls ... telling them that he needed to get to them, they needed to change their story, they were lying on him____ It was for the purpose of inducing a change in their testimony and intimidating them.” Finding “clear obstruction,” the court imposed a two-level enhancement under U.S.S.G. § 801.1.
We review the district court’s findings of fact for clear error, but review de novo its determination that specific facts constitute obstruction of justice under the guidelines. United States v. Williams, 709 F.3d 1183, 1185 (6th Cir.2013).
Rather than seeking to influence either “a witness” or “a witnesses] anticipated testimony,” Jackson argues, he admonished Adrianna about “testimony previously rendered,” which is not obstruction. But the plain language of the guideline, which extends to the “sentencing of the instant offense of conviction,” belies this argument. U.S.S.G. § 3C1.1 (emphasis added). The guideline applies fully to Jackson’s pre-senteneing communications [464]*464with a witness. United States v. Irby, 240 F.3d 597, 600 (7th Cir.2001).
The district court correctly concluded that Jackson attempted to influence Adrianna’s testimony. Jackson accused Adrianna of lying about her prostitution activities no less than four times in his letter. Sandwiched between these accusations, Jackson invites Adrianna to “think of’ what her testimony did to him. The district court quite naturally inferred that Jackson wanted Adrianna to recant and sent the letter to convince her to do so. The trial confirmed that both Jackson and Adrianna knew that she, in fact, prostituted herself. Jackson’s efforts to secure a recantation were therefore efforts to elicit false testimony. See United States v. Cannon, 552 Fed.Appx. 512, 515 (6th Cir.2014) (upholding obstruction enhancement when Cannon asked his wife to tell a “truth” that both knew was “manifestly false”). We discern no error in the obstruction enhancement.
B. Uncounseled Convictions
Next, Jackson argues that the district court counted two uncounseled state-court convictions in his criminal history, resulting in an increased criminal-history category. For both convictions, the pre-sentence report noted that “[attorney representation is unknown.” Pointing to this language, Jackson asserted that the government failed to prove the validity of the convictions and therefore could not count them in his criminal-history score. The district court overruled Jackson’s objection, and we review for clear error. United States v. Adkins, 729 F.3d 559, 569 (6th Cir.2013).
Jackson bears the burden of showing that a prior conviction is invalid because of a failure to appoint counsel in violation of Gideon v. Wainwright, 372 U.S. 335, 83 S.Ct. 792, 9 L.Ed.2d 799 (1963). United States v. Kitchen, 428 Fed.Appx. 593, 598 (6th Cir.2011). But rather than denying representation, Jackson merely presses the lack of documentation. Given Jackson’s silence on the point, we examine it no further.
C. Failure to Explain
Jackson objected to the following two-level guidelines enhancements: (1) “unduly influenc[ing] a minor to engage in prohibited sexual conduct” and (2) “the commission of a sex act or sexual contact” in connection with sex trafficking children. U.S.S.G. §§ 2G1.3(b)(2)(B), (b)(4)(A). He argued that the age difference between him and the victims insufficiently supported the undue-influence enhancement and that the sex-act enhancement was “subsumed within the charge of conviction.” The district court tersely overruled these objections at sentencing, and Jackson now claims that the “barren” record prevents meaningful appellate review.
In handing down a sentence, the district court must satisfy us that it “considered the parties’ arguments and has a reasoned basis for exercising [its] own legal decisionmaking authority.” Rita v. United States, 551 U.S. 338, 356, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007). Here, the district court briefly but adequately explained why it rejected Jackson’s objection to the undue-influence enhancement. It found the enhancement “appropriate” due to the age difference between twenty-nine-year-old Jackson and his teenaged victims. See U.S.S.G. § 2G1.3 cmt. n. 3(B) (“In a case in which a participant is at least 10 years older than the minor, there shall be a rebuttable presumption that [the enhancement] applies.”). And when summarizing the case, the court elaborated on the undue influence, noting for example, Jackson’s provision of vodka.
[465]*465As to the sex-act enhancement, the court noted that sex acts “could be subsumed” in the charged offense of sex trafficking. But, as the government argued, sex need not actually occur. Jackson completed the offense when he transported the victims knowing that a sex act “will be caused in the future.” True, the court could have explained its ruling in greater detail, but Jackson suffered no prejudice. The record and our case law allow the enhancement. See, e.g., Willoughby, 742 F.3d at 241 (6th Cir.2014) (affirming the enhancement because “a sex act does not have to occur to satisfy the elements of the child-sex-trafficking offense”).
The court explained why it imposed the enhancements, the record supports them, and there was therefore no error.
D. Substantive Reasonableness
We afford a within-guidelines sentence a rebuttable presumption of reasonableness. United States v. Callahan, 801 F.3d 606 (6th Cir.2015). Jackson’s 360-month sentence fell at the low end of the advisory guidelines range, and he advances no arguments on appeal to rebut the presumption of reasonableness.
IV.
We AFFIRM Jackson’s conviction and sentence.