ORDER

Jeffrey Hill, convicted of capital murder and sentenced to death by the State of Ohio, has filed a rehearing petition regarding our recent affirmance of a district court decision denying his petition for a writ of habeas corpus. In rejecting the rehearing and rehearing en banc petition, the panel writes briefly to address two points raised in it.

First, Hill asserts that the panel erred in rejecting the claim that his counsel provided ineffective assistance by failing to prepare Hill before he testified during the mitigation phase of his trial. In rejecting this claim (and three others), we explained that Hill had failed

to come to grips with the district court’s decisions on each of these points. In rejecting these claims, the district court *598did not address the merits of the claims but instead dismissed the claims as procedurally defaulted. JA 241 — 42, 242— 43, 3451, 240. Nonetheless, in his briefs on appeal, Hill does not challenge the district court’s rulings on procedural default, see Hill Br. at 99 — 101, 101 — 104, 32 — 35, 60, but argues only the merits of the claims. Under these circumstances, he has waived his right to challenge these components of the district court’s decision. See Spirko v. Mitchell, 368 F.3d 603, 612 (6th Cir. 2004) (explaining, in a death penalty case, that “[i]t is a settled appellate rule that issues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived”) (quotation marks omitted); Hutchison v. Bell, 303 F.3d 720, 748 n. 7 (6th Cir. 2002) (concluding, in a death penalty case, that defendant’s “other claims of ineffective assistance of counsel have not been adequately briefed. Hence, we find them to be waived.”).

400 F.3d 308, 335. In response, Hill claims that he addressed the procedural default ruling, arguing that pages 34 through 35 of his appellate brief did just that. But as the quoted passage shows, we specifically considered those pages of his brief, and we concluded then (and we conclude now after another review of that section of his brief) that he failed adequately to challenge the procedural default ruling. At most, he quotes from an affidavit that could be used to make such an argument. Nothing in the cited pages asserts that he did not procedurally default the claim. Instead, when addressing this claim he appears to make a merits argument, namely that his counsel was ineffective under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

Second, Hill argues that we incorrectly dismissed another ineffective-assistance claim — that his counsel failed to prepare two witnesses who testified on his behalf during the mitigation hearing — on the ground that Hill did not obtain a certificate of appealability for this claim. Even if the district court’s certifieate-of-appealability rulings may fairly be said to cover this claim (and on further reflection we think that they can be), that does not affect the judgment in this case. In our prior opinion, we rejected his related claim that “his lawyers failed to provide effective assistance by not presenting the testimony of additional family and friends during the mitigation proceeding.” 400 F.3d at 331. Nothing in the proposed testimony, we reasoned, “differs in such a material way as to establish that Hill was prejudiced by the omission of this testimony.” Id. at 331.

His failure-to-prepare-witnesses claim fails for similar reasons. Hill argues that his cousin, Robin Hill, presented very little testimony. While he is correct that she had little to say, he does not explain what testimony she would have presented had she been prepared more effectively or how that testimony would have differed materially from the evidence that the jury did consider.

Nor does Hill explain what affirmative testimony Shawonar Head, the mother of his daughter, would have presented had she been prepared more effectively. Instead, he argues that Head’s testimony undercut his mitigation-phase testimony about the amount of child support he provided to their daughter. Head and Hill both agreed that he provided child support for their daughter, and no one disputed that Hill gave a portion of his settlement proceeds from several vehicle accidents *599(totaling $30,000) to his mother and that the money was in fact kept in his mother’s bank account. The apparent inconsistency arose because Hill also testified that some of the settlement proceeds went to child support and Head testified that she did not see any of this money but rather received a portion of Hill’s earnings (for child support) during this time. Even if Hill’s counsel should have avoided asking Head about the settlement money (or, better yet, ascertained how she could know the financial sources from which Hill provided child support), Hill was not prejudiced by Head’s testimony. For one, the evidence does not preclude the possibility that the settlement money was directed for child support in the event that Hill pre-deceased his child or Head. For another, Head’s testimony does not eliminate the possibility that she received a meaningful amount (indeed, even an equivalent amount) of child support from Hill during this time, though from his salary rather than from insurance proceeds. For still another, it would defy logic to believe that the jury would have balanced the aggravating factor (Hill’s aggravated murder of his mother by stabbing her and then robbing her) against the mitigating factors Hill presented (that he was in a state of cocaine psychosis when he committed the murder, that he confessed to the murder, that he had a difficult childhood, that he could be rehabilitated, and that he had done good deeds in the past, such as working with handicapped children and paying support for Head and their daughter) differently merely had they not known that he provided a smaller amount of child support than he originally claimed or that he provided the same amount of child support but from a different source.

For these reasons and for those stated in our prior opinion, Hill v. Mitchell, 400 F.3d 308 (6th Cir. 2005), we deny Hill’s rehearing and rehearing en banc petition.