ORDER
Dale Allen Hurick, a pro se Michigan prisoner, appeals from the district court’s denial of his 28 U.S.C. § 2254 petition for a writ of habeas corpus. He seeks a certificate of appealability (“COA”) from this court and moves for reconsideration of the denial of his motion for leave to obtain discovery.
In 2009, a jury convicted Hurick of first-degree premeditated murder, and the court sentenced him to life in prison without parole. People v. Hurick, No. 295538, 2011 WL 521189, at *1 (Mich. Ct. App. Feb. 15, 2011). The conviction arose from the fatal beating of Jason Watson. Watson and Hurick were long-time acquaintances who spent the night leading up to the murder drinking with friends at several Detroit bars. In the early hours of the next morning, the two left for Hurick’s home and continued to drink. Hurick’s housemate, Francisco Saadedra, testified that when the two men later left the home, he noticed that Hurick had “some kind of tool like a hammer or screwdriver or something.” Saadedra hadn’t noticed the tool when the men arrived or when Hurick returned alone, ten to fifteen minutes later. In addition, Saadedra and his brother-in-law, Richard Bowles—another housemate—both recalled seeing Hurick immediately change his clothes and clean his hands and face when he returned and remembered red liquid on Hurick’s shoes and hands. Bowles refused to testify at trial, so his testimony from the preliminary examination was read into the record. He reported that Hurick told him that he had “fucked dude up pretty good” with “a stone or brick or something like that.”
Watson was found the next day with dozens of lacerations indicating blunt force trauma, numerous fractures to his face and the top, back, and inside of his skull, and damage to both sides of his brain. Hurick was taken into custody and, after waiving his rights under Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), was interviewed by police. Eventually, Hurick authored a written statement that accused Bowles of masterminding the attack and admitted that he—Hurick—had only hit Watson twice with a hammer before Bowles took it and hit Watson three more times in the face. According to Hur-ick, the two men fled but later returned to the scene to find that Watson was still breathing. At that point,' Hurick wrote in his statement, Bowles smashed Watson’s face with a rock.
Prior to trial, Hurick was evaluated for competency to stand trial or to waive his Miranda rights, as well as for criminal responsibility. There is apparently no dispute that Hurick was found competent in all three tests. However, ten days before trial was set to begin, Hurick moved to adjourn so that he could obtain an inde*523pendent evaluation. The trial court refused to delay the trial and denied Hurick’s two subsequent oral motions for adjournment. The court also denied Hurick’s motion for an adjournment to accommodate an evi-dentiary hearing to test the voluntariness of his inculpatory statement.
On direct appeal, Hurick raised three claims: that the court improperly denied his motions for adjournment to test (1) his competency and (2) the voluntariness of his written statement; and (3) the evidence was insufficient to establish first-degree murder. The Michigan Court of Appeals affirmed, and the Michigan Supreme Court denied leave to appeal. People v. Hurick, 489 Mich. 992, 800 N.W.2d 588 (2011). Hurick then filed a motion for relief from judgment under Michigan Court Rule 6.500, alleging (4) judicial bias; (5) improper admission of Bowles’s preliminary-examination testimony; (6) unconstitutional arrest; (7) involuntary waiver of his Miranda rights; and (8) ineffective assistance of trial counsel. That motion was denied by the trial court, and the Michigan Court of Appeals and Michigan Supreme Court both denied leave to appeal.
In 2014, Hurick filed this § 2254 petition, raising the eight grounds advanced on direct appeal and in his Rule 6.500 motion, and adding (9) ineffective assistance of appellate counsel. The magistrate judge recommended denying relief as to all nine grounds. Over Hurick’s objections, the district court adopted the report and recommendation and denied the petition. Hurick now seeks a COA from this court.
A COA may be issued “only if the applicant has made a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). To satisfy this standard, the applicant must demonstrate that “jurists of reason could disagree with the district court’s resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.” Miller-El v. Cockrell, 537 U.S. 322, 327, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). Where the district court has denied the petition on procedural grounds without reaching the underlying constitutional claims, the petitioner must demonstrate that reasonable jurists “would find it debatable whether the petition states a valid claim of the denial of a constitutional right and ... would find it debatable whether the district court was correct in its procedural ruling.” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000).
Where the state courts adjudicated the petitioner’s claims on the merits, the relevant question is whether the district court’s application of 28 U.S.C. § 2254(d) to those claims is debatable by jurists of reason. See Miller-El, 537 U.S. at 336-37, 123 S.Ct. 1029. Under § 2254(d), habeas corpus relief may be granted on claims that were adjudicated in state court only if (1) the state-court adjudication “was contrary to, or involved an unreasonable application of, clearly established [fjederal law,” or (2) the state-court adjudication “was based on an unreasonable determination of the facts.” 28 U.S.C. § 2254(d).
Hurick first asserts that the trial court erred in denying his motion for adjournment to independently test his competency to stand trial, competency to waive his Miranda rights, and his criminal responsibility. The “[djenial of a continuance rises to the level of a constitutional violation only if it is so arbitrary as to violate due process.” Foley v. Parker, 488 F.3d 377, 389 (6th Cir. 2007). “The petitioner must also demonstrate that the denial of a continuance actually prejudiced his or her defense.” Id.
*524The Michigan Court of Appeals denied Hurick’s first claim because he failed to “present any evidence suggesting that he labored under a mental defect or disease that could affect his culpability or capacity” such that an independent evaluation was necessary. Hurick, 2011 WL 521189, at *2. The district court agreed.
The reasons Hurick’s counsel proffered at trial—“he has a closed head injury as well as there is some schizophrenia. And I’m getting this from the family. And I’ve had conversations with [defendant] ... and it’s a little difficult to communicate with him”—were not supported by medical records, testimony, or affidavits. More to the point, Hurick had already obtained a culpability and capacity evaluation; he provided no basis for concluding that it was biased, inaccurate, or otherwise defective such that independent review was required. - It cannot be said that the trial court’s denial of Hurick’s motion was arbitrary when he had already obtained one evaluation and there was no concrete evidence that a second was necessary. Reasonable jurists would not debate the district court’s conclusion that the Michigan Court of Appeals reasonably applied clearly established federal law.
In his second ground, Hurick argued that the court violated his due process rights by denying his motion to adjourn the trial for an evidentiary hearing to test whether his inculpatory statement to the police was voluntary.
The Michigan Court of Appeals rejected the second ground because Hurick never challenged the admissibility of the statement at trial. In fact, Hurick did not object even when a video recording of his interviews was shown to the jury. It was not until Hurick’s Rule 6.500 post-conviction motion that he even mentioned the volun-tariness issue. The district court concluded that the state court’s analysis was reasonable. Reasonable jurists would not dispute the district court’s conclusion: Because Hurick failed to even question the admissibility of the statement, the trial court’s denial of his motion for an adjournment to hold an evidentiary hearing was not arbitrary.
Hurick waives his third ground by not including it in his application for a COA. See Jackson v. United States, 45 Fed.Appx. 382, 385 (6th Cir. 2002) (habeas petitioner who does not appreciably brief an issue waives it).
In his fourth ground, Hurick asserts that the trial judge was biased. He complained of “comments which were adverse to [his] ability to properly defend himself” and asserted that “many of the orders and opinions made by the trial [c]ourt were based on a biased personal opinion of [Hurick.]”
A defendant has a right to a trial before an impartial judge. Tumey v. State of Ohio, 273 U.S. 510, 535, 47 S.Ct. 437, 71 L.Ed. 749 (1927). But comments that do not exhibit favoritism or antagonism for a party are insufficient to establish judicial bias. See Liteky v. United States, 510 U.S. 540, 555, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994). Likewise, judicial rulings almost never constitute a valid basis for a finding of judicial bias. Id. The trial court found no evidence of judicial bias when it reviewed Hurick’s Rule 6.500 motion, and the district court concluded that that determination was a reasonable application of federal law.
Reasonable jurists would not dispute that conclusion. Hurick’s entire argument in support of relief on this ground is premised on the trial court’s improper denial of his motions for time to conduct a competency evaluation and evidentiary hearing, and statements made along the way. But those denials were reasonable, and, as Li-*525teky makes clear, mere adverse rulings are not by themselves enough to support habe-as relief.
Hurick waives his fifth ground by failing to raise it in his application for COA. See Jackson, 45 Fed.Appx. at 385.
In his sixth ground, Hurick. argues that his arrest violated the Fourth Amendment because his arrest warrant was issued without a probable cause determination. The district court rejected this ground in light of Stone v. Powell, 428 U.S. 465, 494, 96 S.Ct. 3037, 49 L.Ed.2d 1067 (1976), which holds that habeas relief is unavailable to a state prisoner who alleges that his conviction was based on an illegal seizure when the state courts provided an acceptable mechanism by which to challenge the seizure. Habeas relief is possible only when the Fourth Amendment claim is “frustrated by a failure of that mechanism.” Gilbert v. Parke, 763 F.2d 821, 823 (6th Cir. 1985).
Reasonable jurists would not debate the district court’s rejection of this claim. Not only does Michigan provide an adequate avenue to raise a Fourth Amendment claim, but Hurick himself raised such a claim in his Rule 6.500 motion. The trial court addressed the claim and denied it. Hurick provides no basis to conclude that his claim was frustrated by a failure in Michigan’s Fourth-Amendment-review mechanism.
In his seventh ground, Hurick alleges that his statement to police should have been suppressed as the result of police coercion. Certain interrogation techniques “are so offensive to a civilized system of justice that they must be condemned under the Due Process Clause of the Fourteenth Amendment.” McCalvin v. Yukins, 444 F.3d 713, 719 (6th Cir. 2006) (quoting Miller v. Fenton, 474 U.S. 104, 109, 106 S.Ct. 445, 88 L.Ed.2d 405 (1985)). Ultimately, the inquiry is “whether [the] defendant’s will was overborne at the time he confessed.” Id.; Ledbetter v. Edwards, 35 F.3d 1062, 1067 (6th Cir. 1994). To make this determination, the court looks at the totality of the circumstances surrounding the confession, including such factors as the defendant’s age, education, and intelligence; whether the defendant has been informed of his constitutional rights; the length and extent of the questioning; and the use of physical punishment, such as deprivation of food or sleep. McCalvin, 444 F.3d at 719.
Neither the Michigan Court of Appeals nor the trial court found any evidence of police coercion. In the district court, Hur-ick alleged that he was deprived of food, medication, an attorney, and sleep. But the district court confirmed what the Michigan courts had found: there was no credible evidence of coercion. Given that Hurick’s only support was his own self-serving affidavit, he has not shown that the denial of relief on this claim was the result of unreasonable application of law or fact.
In his eighth ground for habeas relief, Hurick argues that his trial counsel was ineffective. To prove ineffective assistance of counsel, a habeas petitioner must show that his attorney’s performance was objectively unreasonable and that he was prejudiced as a result. Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). The standard is “highly deferential,” id. at 689, 104 S.Ct. 2052, and “doubly so” on federal habeas review, Harrington v. Richter, 562 U.S. 86, 105, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011) (citation omitted).
The magistrate judge concluded that Hurick procedurally defaulted this ground by failing to present it on direct appeal. However, because “the cause-and-prejudice analysis adds nothing but complexity *526to the case,” and because the merits of this ground are relevant to a later argument, we “cut to the merits here,” Babick v. Berghuis, 620 F.3d 671, 576 (6th Cir. 2010), as the district court did.
Hurick argued that his three trial attorneys were ineffective for inadequately cross-examining Bowles, failing to challenge his competency, failing to challenge the admissibility of his statement, and failing to challenge the admission of Bowles’s testimony. While the Sixth Amendment guarantees a criminal defendant the right “to be confronted with the witnesses against him,” U.S. Const. amend. VI, the core inquiry is whether the defendant was given an opportunity to “test the credibility of witnesses through cross-examination.” Boggs v. Collins, 226 F.3d 728, 736 (6th Cir. 2000). Here, Hurick was represented at the preliminary hearing, where his attorney thoroughly cross-examined Bowles. See Williams v. Bauman, 759 F.3d 630, 635-36 (6th Cir. 2014). In addition, Hurick has not shown that the competency evaluation he did receive was inaccurate or untrustworthy, and there is no basis to conclude that his statement was the result of police coercion. Reasonable jurists would not debate the district court’s rejection of this ground.
In his ninth and final habeas ground, Hurick argued that his appellate counsel was ineffective for failing to raise the grounds above. In the context of an ineffective-assistance-of-appellate-counsel claim, the Strickland analysis requires a petitioner to show that the omitted claims were “clearly stronger than those presented” on direct appeal. Monzo v. Edwards, 281 F.3d 568, 579 (6th Cir. 2002) (quoting Gray v. Greer, 800 F.2d 644, 646 (7th Cir. 1986)). The district court denied relief on this ground because it found all of the previous grounds lacked merit.
Reasonable jurists would not debate the district court’s conclusion as to Hurick’s first, second, and third grounds, all of which were raised on direct appeal. Hurick, 2011 WL 521189, at *1-6. Likewise, his fourth, fifth, sixth, and seventh grounds are raised only in support of his procedural default argument raised in ground eight. Such “conclusory and perfunctory” ineffectiveness claims are inadequate under Strickland. See Wogenstahl v. Mitchell, 668 F.3d 307, 335-36 (6th Cir. 2012).
Accordingly, Hurick’s application for a COA is DENIED and his motion for reconsideration is DENIED.