KETHLEDGE, J., delivered the opinion of the court, in which COLE, C.J., joined, and GRIFFIN, J., joined in the result. GRIFFIN, J. (pp. 405-09), delivered a separate opinion concurring in the judgment. ■
OPINION
KETHLEDGE, Circuit Judge.John Drummond killed a three month-old girl when he fired an assault rifle at her home. An Ohio jury convicted Drum-mond of murder and sentenced him to death. The Ohio Supreme Court affirmed. Drummond thereafter sought federal ha-beas relief, which the district court granted on the ground that the trial court had violated Drummond’s Sixth Amendment rights when it partially closed the courtroom for the testimony of three witnesses during his trial. A divided panel of this court affirmed, but the Supreme Court vacated our decision and remanded the case for reconsideration in light of White v. Woodall, — U.S. -, 184 S.Ct. 1697, 188 L.Ed.2d 698 (2014). Having thus reconsidered the ease, we reverse the district court’s grant of the writ.
I.
Our prior decision recites most of the relevant facts. See Drummond v. Houk, 728 F.3d 520 (6th Cir.2013). We now recite only the ones necessary to our decision here. For several hours during .Drum-mond’s trial, the trial court closed the courtroom to the public. The court explained that one spectator had been disrespectful to deputies and to the court, that another had been charged with assault on a peace officer after an altercation in the courthouse, that some jurors or witnesses felt threatened by some of the spectators, *402and that Drummond had approached the husband of a potential juror during voir dire. The court allowed the media to remain in the courtroom. During this partial closure, three witnesses testified for the prosecution.
The trial court also limited Drummond’s ability to cross-examine three other witnesses for the prosecution: Nathaniel Morris, Dean Thomas, and James Rozen-blad. Drummond sought to ask each of those witnesses about criminal charges that were either pending against them or had previously been dismissed. The trial court barred those questions, however, because the witnesses had not been convicted of any of the charges.
The jury ultimately convicted Drummond of aggravated murder, among other crimes, and sentenced him to death. The Ohio Supreme Court affirmed on direct review. State v. Drummond, 111 Ohio St.3d 14, 854 N.E.2d 1038 (2006). Drum-mond filed a petition for post-conviction relief in the state trial court, which denied his petition. The Ohio Court of Appeals affirmed. State v. Drummond, No. 05 MA 197, 2006 WL 3849295 (Ohio Ct.App. Dec. 20, 2006). The Ohio Supreme Court declined to hear Drummond’s appeal. State v. Drummond, 113 Ohio St.3d 1512, 866 N.E.2d 512 (2007) (table).
Drummond then filed a habeas petition in federal district court, arguing that the partial closure violated his right to a public trial; that the trial court violated his rights under the Confrontation Clause by limiting his cross examination of Morris, Thomas, and Rozenblad; and that his attorney was constitutionally ineffective during the penalty phase of the trial. The district court denied relief on Drummond’s ineffective-assistance and Confrontation Clause claims, but granted a conditional writ of habeas corpus based on his public-trial claim. Drummond v. Houk, 761 F.Supp.2d 638 (N.D.Ohio 2010).
We affirmed, holding that the Ohio Supreme Court had unreasonably applied the holding of Waller v. Georgia, 467 U.S. 39, 104 S.Ct. 2210, 81 L.Ed.2d 31 (1984). See Drummond, 728 F.3d at 534. One judge dissented. Id. at 543-45. Per the Supreme Court’s remand order, see Robinson v. Drummond, — U.S. -, 134 S.Ct. 1934, 188 L.Ed.2d 957 (2014), we now reconsider the State’s appeal.
II.
Under the Antiterrorism and Effective Death Penalty Act, a court may grant habeas relief only if the state court’s adjudication of the petitioner’s claim “resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United StatestJ” 28 U.S.C. § 2254(d)(1). In Woodall, the Supreme Court made clear that “relief is available under § 2254(d)(l)’s unreasonable-application clause if, and only if, it is so obvious that a clearly established rule applies to a given set of facts that there could be no fair-minded disagreement on the question[.]” 134 S.Ct. at 1706-07 (internal quotation marks omitted).
A.
Unlike this case, Waller concerned a full, rather than partial, closure of the courtroom to the public. (By full closure we mean a closure where the entire public, including the media, is excluded from the courtroom.) But the Supreme Court began its analysis by stating a general rule ' that applies to any type of courtroom closure, to wit: a trial court must balance the interests for and against closure. See 467 U.S. at 45, 104 S.Ct. 2210. The Ohio courts reasonably (in the habeas sense) *403applied that general rule here: the trial court offered serious reasons for the closure and tailored its scope in rough proportion to them; and the Ohio Supreme Court affirmed the trial court’s decision in an opinion that — agree with it or not — -was reasoned and coherent in its application of that general rule.
But Waller also laid down a cluster of more-specific rules — “the party seeking to close the hearing must advance an overriding interest that is likely to be prejudiced, the closure must be no broader than necessary to protect that interest, the trial court must consider reasonable alternatives to closing the proceeding, and it must make findings adequate to support the closure” — that the Court held were applicable to the full-closure at issue there. 467 U.S. at 48, 104 S.Ct. 2210. Drummond argues that the trial court violated those rules: in his view, the closure in his case was broader than strictly necessary, the court’s findings in support of the closure were not as careful and detailed as they should have been, and the court did not make clear the extent to which it considered other alternatives.
Drummond’s arguments are by no means frivolous, as our decision today in a direct-review case makes clear. See United States v. Simmons, — F.3d - (2015). But Drummond’s case comes to us on habeas review rather than direct. Per the Supreme Court’s precedents, therefore, the relevant question is not whether we agree with Drummond’s arguments, but whether any “fairminded jurist” could disagree with them. Woodall, 134 S.Ct. at 1707. In answering that question, we can consider only the Supreme Court caselaw that was already on the books at the time of the Ohio Supreme Court’s decision here. See Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). (We also note that, contrary to Drum-mond’s assertion otherwise, it is by no means clear that the Court’s later decision in Presley v. Georgia, 558 U.S. 209, 130 S.Ct. 721, 175 L.Ed.2d 675 (2010), involved only a partial closure. For in Presley the trial court excluded “the public” rathér than only a part of it. Id. at 210, 130 S.Ct. 721.)
Drummond’s arguments are ■ premised on the assertion that we should extend Waller’s more specific rules — in their entirety, with no alteration — from the full closure at issue there to the partial closure at issue here. What was not obvious at the time of the Ohio Supreme Court’s decision, however — and thus not clearly established for purposes of the habeas statute— is whether and how these more specific rules apply in cases, like this one, where some spectators but not all are removed from the courtroom. The Supreme Court’s caselaw does not clearly establish, for example, whether in such cases the trial court must identify an “overriding” interest favoring closure, as in Waller, or instead only a “substantial” interest, as some circuit courts have inferred, or perhaps even some lesser interest. Likewise unclear — and thus not clearly established — is whether the closure, must be “narrowly tailored,” 467 U.S. at 45, 104 S.Ct. 2210, as the Court required in Waller, or whether in partial-closure cases a somewhat looser cut will do. And on the procedural side, Waller says the court must make “findings adequate to support the closure.” Id. at 48, 104 S.Ct. 2210. But “adequate” is a vague and therefore elastic term; and for all the Ohio courts knew here, “adequate” might mean one thing in full-closure cases, and a different and less rigorous thing when the closure is only partial.
Woodall itself provides some parallels. That case concerned the so-called “no-adverse-inference rule,” which the Supreme *404Court announced in Carter v. Kentucky, 450 U.S. 288, 101 S.Ct. 1112, 67 L.Ed.2d 241 (1981). Per that rule, juries are instructed not to infer, from a defendant’s decision not to testify, that the defendant is guilty. The question in Woodall was whether — “beyond any possibility for fair-minded disagreement[,]” 134 S.Ct. at 1703-the no-adverse-rule applies the same way in the penalty phase as it does in the guilt phase. Our court had answered yes, beyond any fairminded disagreement, the rule applies the same way in both phases. 685 F.3d at 579. But the Supreme Court held the answer was not so clear. In terms applicable here, the Court said that “[t]he critical point is that relief is available under § 2254(d)(l)’s unreasonable-application clause if, and only if, it is so obvious that a clearly established rule applies to a given set of facts that there could be no ‘fairminded disagreement’ on the question[.]” 134 S.Ct. at 1706-07. Then the Court said that “[pjerhaps” the no-adverse-inference rule should apply in the penalty phase exactly as it does in the guilt phase, but “perhaps not.” Id. at 1707. What matters, the Court said, was that “we have not yet taken that step, and there are reasonable arguments on both sides — which is all Kentucky needs to prevail in this AEDPA case.” Id.
The same reasoning applies here. Just as in Woodall, the factual context in the relevant Supreme Court case and the petitioner’s case are meaningfully different: Carter involved the guilt phase, Woodall the sentencing; Waller involved a full closure, Drummond a partial one. And for the reasons discussed above, “there are reasonable arguments,” id., that Waller does not apply to partial-closure cases in the wholesale manner that Drummond says it does. The only principle from Waller that was clearly established for purposes of the partial closure here was the general one that the trial court must balance the interests favoring closure against those opposing it. The Ohio courts applied that principle; and they did so reasonably, in the capacious sense of “reasonable” as used for purposes of the habeas statute. The Ohio Supreme Court’s application of Waller to Drummond’s case therefore was not unreasonable within the meaning of the habeas statute, which means that he is not entitled to relief on this claim.
B.
Drummond also argues that the trial court violated his rights under the Confrontation Clause when it barred him from cross-examining Morris, Rozenblad, and Thomas about pending or previously dismissed criminal charges. But so far the Supreme Court has recognized a defendant’s right to cross-examine a witness about criminal charges only in one circumstance: when the government has agreed to give the witness favorable treatment in exchange for his testimony. Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986). Here, all three witnesses testified that the State had not agreed to any such arrangement in their cases. Thus, the trial court’s decision to bar Drummond from cross-examining Morris, Rozenblad, and Thomas about their criminal history was not contrary to the Supreme Court’s holding in Van Ars-dall. The district court properly denied habeas relief based on Drummond’s Confrontation-Clause claim.
C.
Finally, Drummond argues that he is entitled to relief because his attorney was constitutionally ineffective. Specifically, Drummond says that his lawyer should have interviewed Drummond’s half-brother, Michael Brooks, and called Brooks to testify during the penalty phase of the *405trial. To show a constitutional violation based on ineffective assistance of counsel, a petitioner must show both that his lawyer’s performance fell “below an objective standard of reasonableness,” and that “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Strickland, v. Washington, 466 U.S. 668, 687-88, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
A defense lawyer need not interview every member of a defendant’s family when gathering mitigation evidence. Bobby v. Van Hook, 558 U.S. 4, 9-12, 130 S.Ct. 13, 175 L.Ed.2d 255 (2009). Instead, there “comes a point at which evidence ... can reasonably be expected to be only cumulative, and the search for it distractive from [the attorney’s] more important duties.” Id. at 11, 130 S.Ct. 13.
Here, Drummond’s lawyer retained an investigator and a psychologist to seek out mitigation evidence. And Drummond’s lawyer himself obtained evidence that Drummond was unsupervised as a teenager, that his parents divorced when he was 14, that he stayed with his father, until they had a falling out, that he later moved in with his half-brother, that he had failing grades, that he dropped out of school, and that he joined a gang. Thus, the decision of Drummond’s defense counsel “not to seek more mitigating evidence from the defendant’s background than was already in hand” — by interviewing Drummond’s half-brother as well — “fell well within the range of professionally reasonable judgments.” Id. at 11-12, 130 S.Ct. 13 (internal quotation marks omitted).
Moreover, Brooks’s affidavit merely recites facts about Drummond’s background that the jury already knew. Drummond therefore cannot show a reasonable probability that, if Brooks had testified, the jury would not have sentenced him to death. The district court properly denied relief on this claim.
The district court’s conditional grant of the writ of habeas corpus is reversed. The district court’s judgment is otherwise affirmed.