A Michigan jury convicted petitioner Michael Batey of first-degree criminal sexual conduct for molesting his nephew, and the judge sentenced him to 15 to 45 years. Batey failed to obtain relief in his direct appeals, and he now has been released from prison, though (so far as the record shows) he apparently remains on parole. In this case, Batey appeals the district court’s denial of his petition for a writ of habeas corpus based on an alleged Confrontation Clause violation. The district court rejected the claim. We affirm.
I.
After Michael Batey’s minor nephew Matthew suffered a nervous breakdown, his parents admitted him to a mental health facility. At that point, Matthew’s older brother Jason told his parents that Batey had been sexually abusing Matthew and Jason for several years. Matthew confirmed that the abuse had happened.
The State of Michigan charged Batey with two counts of criminal sexual conduct based on oral and anal sex with Matthew. Batey v. Scutt, 460 Fed.Appx. 530, 531 (6th Cir.2012). At trial, Matthew and Jason testified that Batey had abused them. Id. The boys’ mother Sandra testified that Matthew’s behavior had worsened leading up to his breakdown, and she confirmed that, after the episode, Jason revealed Ba-tey’s abuse.
Batey’s primary defense was that Matthew and Jason’s parents manufactured the abuse accusations because he is gay and because he had encouraged the boys to explore their homosexual feelings. Ba-tey, 460 Fed.Appx. at 531. Batey also argued that it was Jason who had sexually abused Matthew. Id. Jason, as it turned out, had molested his younger brother, and he told the police as much at the time he accused Batey. Fearing a confusing “fishing expedition” and an unduly prejudicial sideshow about Matthew’s sexual history, the trial court granted the State’s motion in limine prohibiting any exploration of Matthew and Jason’s sexual history with each other in accordance with Michigan’s rape-shield law. Batey, 460 Fed.Appx. at 531. Batey still was permitted to challenge the boys’ credibility on other fronts. He exposed their shared mental health *592issues, some inconsistencies in their testimony, and their recall problems. Batey also highlighted Jason’s history of drag and alcohol abuse as well as his tendency to lie.
The jury eventually convicted Batey on the oral sex charge, but it acquitted him of the anal sex charge. Batey, 460 Fed.Appx. at 583. He was sentenced to 15 to 45 years in prison. Id. His direct appeals and state court collateral appeals came to naught. People v. Batey, 227117, 2003 WL 23104615 (Mich.Ct.App. Dec. 30, 2003); People v. Batey, 471 Mich. 882, 686 N.W.2d 487 (2004).
Meanwhile, Batey filed a pro se petition for a writ of habeas corpus in federal district court in 2005. See 28 U.S.C. § 2254. He raised six constitutional arguments: (1) juror misconduct during voir dire; (2) destruction of Brady material; (3) withholding of Brady material; (4) undue restrictions on closing argument in violation of the right to a fair trial under the Sixth Amendment; (5) exclusion of certain photos needed for impeachment; and (6) improper questioning and closing argument by the prosecution. Because Ba-tey did not exhaust several of these claims in state court, the district court held the habeas proceedings in abeyance pending consideration of them in the state courts.
After Batey raised many of these claims in the state courts, all to no avail, the district court reopened the federal case, and allowed Batey to add a seventh claim based on ineffective assistance of counsel. The court granted relief on three claims: undue restrictions on the closing argument (the fourth claim), improper prosecution comments (the sixth claim), and ineffective assistance of counsel (the seventh claim). We reversed on each ground and remanded with instructions for the district court to consider the four remaining claims. Batey, 460 Fed.Appx. at 538. On remand, the district court gave Batey leave to supplement his fourth claim — the closing argument claim that we had rejected — to consider whether the State violated his Confrontation Clause rights by limiting the cross-examination of his accusers about Jason’s abuse of his brother Matthew. The district court then rejected that claim along with the rest of Batey’s claims and denied a certificate of appealability for any of the claims. Our court granted a certificate of appealability on the reconfigured fourth claim — now a Confrontation Clause claim.
II.
Batey filed his habeas petition after the Antiterrorism and Effective Death Penalty Act went into effect in 1996. That means we generally review all aspects of the claim through a deferential lens, granting relief only if the state court of appeals’ decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d). Claims not addressed by the state court, however, do not receive deference. Id. In this case, it is not clear whether we should treat the Michigan Court of Appeals’ decision as resolving Batey’s confrontation claim on the merits. In the end, the standard of review does not matter with respect to the merits of the Confrontation Clause claim because it fails even after a fresh look. Traditional habe-as deference, all of the parties agree, applies to the question of harmless error.
Supplementing the fourth claim. The first obstacle to Batey’s claim is that it is difficult to understand how he had a right to supplement a rejected claim. In the first appeal, we rejected Batey’s fourth habeas claim. Batey presented that claim to us, as he had in his complaint and as he had before the district court, as a Sixth *593Amendment fair trial claim that the trial court had unfairly restricted Bateas counsel in making a closing argument about Jason’s motive to lie, namely that Jason had abused Matthew sexually and was trying to shift blame for the abuse and Matthew’s breakdown to Batey. Batey, 460 Fed.Appx. at 536-37; Batey v. Burt, No. 05-73699-DT, 2010 WL 2650019, at *4-7 (E.D.Mich. June 30, 2010). We rejected that claim on harmless-error grounds. Batey, 460 Fed.Appx. at 537. After rejecting this claim and two others, we remanded the case to the district court “to consider whether habeas relief is warranted on the other, previously unconsidered claims raised in Petitioner’s habeas petition.” Id. at 538 (emphasis added). We did not say that the district court could supplement one of the rejected claims by converting it into a Confrontation Clause claim under the Sixth Amendment, as opposed to a fair-trial claim under the Sixth Amendment. Nor of course did we say that the claimant could add new claims well after the statute of limitations had run. See 28 U.S.C. § 2244(d)(1).
The Confrontation Clause. The second problem is that the claim fails on the merits. “In all criminal prosecutions,” the Sixth Amendment provides, “the accused shall enjoy the right ... to be confronted with the witnesses against him.” U.S. Const, amend. VI; Pointer v. Texas, 380 U.S. 400, 403-05, 85 S.Ct. 1065, 13 L.Ed.2d 923 (1965) (applying that guarantee to the States through the Fourteenth Amendment). Batey says that the Michigan trial court’s application of the rape shield law violated his confrontation right by barring him from questioning his accusers about their motives to shift the blame for Jason’s abuse of his brother Matthew. He is correct that the Constitution as a general matter protects a defendant’s right to cross-examine his accusers about potential sources of bias or motives to lie. Davis v. Alaska, 415 U.S. 308, 316-17, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). But neither the Confrontation Clause nor the Due Process Clause guarantees cross-examination “in whatever way, and to whatever extent, the defense might wish.” Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986) (internal quotation marks omitted). The state court in this instance permissibly limited the scope of cross-examination for at least four reasons.
First, Michigan has authority to enact a rape-shield law, the purpose of which is to limit inquiry, including cross-examination, about the sexual history of a victim of sexual abuse. As the Supreme Court has told us — in the context of a constitutional challenge to Michigan’s rape-shield law no less — the Michigan statute “represents a valid legislative determination that rape victims deserve heightened protection against surprise, harassment, and unnecessary invasions of privacy.” Michigan v. Lucas, 500 U.S. 145, 149-50, 111 S.Ct. 1743, 114 L.Ed.2d 205 (1991). Sometimes the right to present relevant testimony must “bow to accommodate other legitimate interests,” such as the privacy rights of victims of sexual abuse. Id. at 149, 111 S.Ct. 1743 (quotation omitted). A first premise for resolving this dispute, then, is that Michigan’s rape-shield law serves legitimate governmental interests.
Second, in applying the rules of evidence, including a State’s rape-shield law, state trial judges “retain wide latitude” to impose reasonable limits on a defendant’s cross-examination of an adverse witness “based on concerns about ... harassment, prejudice, confusion of the issues, the witness’ safety, or interrogation that is repetitive or only marginally relevant.” Id. (internal quotation marks omit*594ted). To show that a judge has exceeded that latitude in the context of an as-applied challenge to the scope of cross-examination on Confrontation Clause grounds, the litigant must show that the exclusion of testimony was “arbitrary or disproportionate” to its purposes. Id. at 151, 111 S.Ct. 1743 (quoting Rock v. Arkansas, 483 U.S. 44, 56, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987)); see also United States v. Scheffer, 523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998). All that is required in other words is that any limitation on cross-examination be reasonable. Otherwise, every restriction on questioning would turn into a mini-constitutional inquiry, subverting the long-held view that the Confrontation Clause is not the font of “a vast and precise body of constitutional common law controlling the particulars of cross-examination.” Dorsey v. Parke, 872 F.2d 163, 166 (6th Cir.1989) (quotation omitted); see also Scheffer, 523 U.S. at 308, 118 S.Ct. 1261 (“[S]tate and federal rulemakers have broad latitude under the Constitution to establish rules excluding evidence from criminal trials.”). So long as the trial judge reasonably concludes that the State’s interest in exclusion outweighs the defendant’s need for the evidence, the Constitution permits the rape shield to do its intended work. See Gagne v. Booker, 680 F.3d 493, 514 (6th Cir.2012) (en banc plurality) (“[T]he trial court must balance a state’s interest in excluding certain evidence under the rape shield statute against a defendant’s constitutionally protected interest in admitting that evidence, on a case-by-case basis— neither interest is superior per se.”).
Third, the state trial judge reasonably balanced the competing factors at play in this case. The considerations include: (1) the potential for distracting “minitrials” on collateral issues, especially the victim’s sexual history; (2) the probative value of the testimony; (3) its “prejudicial or inflammatory nature”; (4) any cautionary instructions or limits on the scope of questioning; and (5) the extent to which the defendant was otherwise able to cross-examine the witness. Jordan v. Warden, Lebanon Corr. Inst., 675 F.3d 586, 595 (6th Cir.2012) (internal quotation marks and citations omitted); see Michigan, 500 U.S. at 149, 111 S.Ct. 1743 (discussing the need to avoid “harassment, prejudice, confusion of the issues ... or interrogation that is repetitive or only marginally relevant”).
Most of these factors support the trial court’s ruling. The potential costs of marching down the path of Jason’s and Matthew’s sexual history were high. Cross-examination about the topic risked getting bogged down in a disruptive mini-trial over the details of that abuse and the explanations for it, making reasonable the trial judge’s fear that allowing cross-examination about the sexual history between the brothers would “mislead or confuse the issues.” R. 18 at 27-28. The inquiry, as the trial judge noted, also risked doing nothing more than allowing the defense to try to paint the brothers as “bad kids.” Id. at 26-28.
By comparison, the net potential benefits to Batey of cross-examination about Jason’s abuse were not high and potentially counter-productive. The unlikely threat that the prosecutor would charge Jason gave him and his family little incentive to lie, and the extensive attacks on Jason and Matthew’s reliability — that were made during the trial — reduced whatever probative value their sexual relationship otherwise might have offered. As to bias, the probative value of exploring Jason’s history was small because the police and prosecution were already well aware of his admitted sexual activity with his brother. And even if Jason’s abuse of his brother had some tendency to show potential bias *595against Batey, the marginal probative value of Jason and Matthew’s sexual relationship as to their credibility remained slight. Both brothers were otherwise thoroughly impeached with their mental instability, and Jason, in particular, with his alleged penchant for lies. Worst of all, as we noted the last time the case came before us, the “unusual nature” of the brothers’ incestuous relationship created a double-edged sword for Batey. Yes, it could show that Batey did nothing—that none of the alleged 25 incidents of oral sex with Matthew ever happened. But it also could have corroborated Matthew’s testimony that Batey groomed him to accept sexual activity between family members as normal. See Batey v. Scutt, 460 Fed.Appx. 530, 537 n. 3 (6th Cir.2012). All of this would have made Matthew and Jason victims of Batey’s abuse, doing far more to undermine Batey’s defense than to advance it.
On this record and in view of these considerations, the trial judge’s application of Michigan’s rape-shield statute was not unreasonable—or, as is sometimes said, “arbitrary or disproportionate.” Batey’s as-applied challenge to the statute on Confrontation Clause grounds fails.
Harmless error. The third obstacle is the harmlessness of any error. Even if the trial court’s application of the rape-shield law violated Batey’s constitutional rights, he still would not be entitled to relief. On direct review, an error may be excused only if it “was harmless beyond a reasonable doubt.” Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). On federal habeas review, that decision receives deference in light of “concerns about finality, comity, and federalism,” something that was true before AEDPA and remains true after its passage. Fry v. Pliler, 551 U.S. 112, 116, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007). The test for harmlessness under § 2254(d) is not simply whether the state court applied Chapman unreasonably. Id. at 119— 20, 127 S.Ct. 2321. Batey may obtain relief only if his asserted error had a “substantial and injurious effect” on the jury’s verdict. Id. at 121, 127 S.Ct. 2321 (quoting Brecht v. Abrahamson, 507 U.S. 619, 631, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)); see also Ruelas v. Wolfenbarger, 580 F.3d 403, 412 (6th Cir.2009) (“Brecht is always the test, and there is no reason to ask both whether the state court ‘unreasonably’ applied Chapman under the AEDPA and, further, whether the constitutional error had a ‘substantial and injurious’ effect on the jury’s verdict.”).
To determine whether limitations on cross-examination affected the jury’s verdict, we consider several things: (1) “the importance of the witness’ testimony”; (2) whether that testimony was “cumulative”; (3) corroborating or contradictory testimony; (4) “the extent of cross-examination otherwise permitted,” and (5) the “overall strength” of the State’s case. Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431; Vasquez v. Jones, 496 F.3d 564, 575 (6th Cir.2007). Measured by these factors, we see no reversible error in the state court’s harmlessness conclusion.
The impeachment evidence, as we noted the last time around, managed to get admitted anyway, meaning that “the questioning that was barred was not aimed at eliciting any additional facts” and thus meaning that any alleged error made far less of a difference than if it had never been admitted. Dorsey, 872 F.2d at 166. Despite the trial court’s ruling under Michigan’s rape-shield law, “the jury had access to evidence that Jason had sexually abused Matthew in the past,” from which it could have inferred the very bias Batey wished to show. Batey, 460 Fed.Appx. at *596537. During an interview of Batey by police, played for the jury, the officer says that Jason admitted to sexual activity with his brother. The prosecution also admitted a letter from Matthew to Batey in which Matthew alleges that his brother molested him. Defense counsel during closing argument also read this portion aloud to the jury before being interrupted by an objection from the government. That objection was sustained, but the trial court did not instruct the jury to ignore defense counsel’s comments or the underlying evidence. Even after the objection was resolved, Batey’s attorney implored the jury to read Matthew’s letter carefully. Here is what we said in the last appeal— there in rejecting Batey’s claim that the trial court unfairly cut off his closing argument on this topic and in finding that the trial court’s error was harmless:
We agree that any error in this case was harmless under Brecht. By virtue of the prosecutor’s earlier admissions, the jury had access to evidence that Jason had sexually abused Matthew in the past. Furthermore, defense counsel was able to read aloud the most damaging portions of this evidence before the prosecutor objected. In fact, defense counsel was able to fully argue that Dr. Zollar’s testimony merely established that Matthew had been a victim of sexual molestation and that the jury could ultimately infer that Jason, not Petitioner, was the perpetrator of that abuse. Although the trial court sustained the prosecutor’s objection, it never instructed the jury to disregard defense counsel’s comments. Finally, defense counsel was able to conclude his closing argument remarks on the subject, without objection, by encouraging the jury to reference Matthew’s letter for itself. We are confident that this directive, coupled with the aforementioned factors, ameliorated any prejudice caused by the trial court’s ruling.
Batey, 460 Fed.Appx. at 537.
A similar conclusion applies here. Between the taped interview and Matthew’s own words, the jury had a basis for assessing the defendant’s theory of bias. Cross-examination about Matthew and Jason’s sexual history thus would not have elicited any new facts from which the jury could have inferred a motive to lie. Even if questioning about the brothers’ sexual history had been permitted, a reasonable jury would not “have received a significantly different impression of [the witnesses’] credibility.” Van Arsdall, 475 U.S. at 680, 106 S.Ct. 1431.
As suggested above, moreover, the probative value of evidence about Jason’s molestation of his brother was marginal. Defense counsel already had ample opportunities to cross-examine Matthew and Jason, and otherwise significantly attack the accuracy of their testimony. Batey cross-examined both brothers about their mental health problems, about hearing voices, and about taking medication for these health problems. Matthew even admitted on cross-examination to hearing voices during trial. Defense counsel explored inconsistencies in the boys’ accounts of the alleged abuse. Acknowledging that Jason had a tendency to lie, his own mother revealed that he had once recanted, claiming he made up the allegations against Batey. All of this testimony cut in the same direction that the between-sibling molestation would have cut — that the brothers, Jason included, could not be trusted to give a reliable account about what had happened. And, worse, it created the risk that the brothers’ sexual activity corroborated Matthew’s account that *597Batey assured him sex between relatives was normal. The net effect of letting in the disputed testimony ran the very real risk of bolstering the boys’ credibility, not undermining it. Batey, 460 Fed.Appx. at 537 n. 3. Any error was harmless under Brecht.
III.
For these reasons, we affirm.