SILER, J., delivered the opinion of the court, in which GRIFFIN, J., joined. CLAY, J. (pp. 439-40), delivered a separate concurring opinion.
OPINION
SILER, Circuit Judge.
A state court jury convicted Frederick Treesh of aggravated murder and several other charges, and the court sentenced him to death. The Ohio courts upheld his conviction and sentence on direct review and in post-conviction proceedings. Treesh petitioned the U.S. District Court for the Northern District of Ohio for a writ of habeas corpus under 28 U.S.C. § 2254. The district court denied the petition but granted Treesh a certificate of appealability (“COA”) on two of his claims. Treesh appeals those claims and requests that we grant a COA as to a third claim. For the following reasons, we AFFIRM the district court’s denial of Treesh’s petition, and DENY his request for an expanded COA.
I. FACTUAL AND PROCEDURAL BACKGROUND
On direct appeal, the Ohio Supreme Court related the facts of the case in State v. Treesh, 90 Ohio St.3d 460, 739 N.E.2d 749, 756-58 (2001), which will not be fully repeated herein.
A. Direct Appeal
Before trial, Treesh filed a motion to suppress his statements as violating Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). After a sup[428]*428pression hearing, the trial court summarily denied Treesh’s motion in a one-sentence order. The jury found Treesh guilty of five counts: aggravated felony murder, aggravated robbery, felonious assault of a peace officer, and two counts of attempted aggravated murder. Each of the five counts included a firearm specification and Treesh pleaded guilty to one count of carrying a weapon under disability. The trial court adopted the jury’s sentence recommendation of death.
The Ohio Eleventh District Court of Appeals affirmed Treesh’s conviction and sentence. In particular, it rejected Treesh’s arguments that the trial court erred in not suppressing his statements and that trial counsel was ineffective by failing to challenge for cause the jurors at issue here. State v. Treesh, No. 95-L-057, 1998 Ohio App. LEXIS 4886, at *25-45, 123-25 (Ohio Ct.App. Oct. 16, 1998). Treesh appealed to the Supreme Court of Ohio raising, inter alia, the two claims presented here. The Ohio Supreme Court rejected both claims, Treesh, 739 N.E.2d at 763-67, 779, and the United States Supreme Court denied Treesh’s petition for a writ of certiorari, Treesh v. Ohio, 533 U.S. 904, 121 S.Ct. 2247, 150 L.Ed.2d 234 (2001).
B. State Post-Conviction Proceedings
The state trial court summarily dismissed Treesh’s petition for post-conviction relief without an evidentiary hearing. On appeal, the Ohio Eleventh District Court of Appeals affirmed the trial court’s denial of post-conviction relief. State v. Treesh, No. 97-L-080, 1998 WL 964528, at *9 (Ohio Ct.App. Dec. 18, 1998). The Ohio Supreme Court summarily dismissed Treesh’s appeal, concluding that it did not present a substantial constitutional question. State v. Treesh, 85 Ohio St.3d 1476, 709 N.E.2d 848 (1999).
C. Federal Habeas Corpus Proceedings
In 2002, Treesh filed the instant petition for writ of habeas corpus. The district court denied Treesh’s petition, Treesh v. Bagley, No. 1:02 CV 462, 2007 WL 1039081, at *64 (N.D.Ohio Mar.31, 2007), and granted a COA as to Claims 2 (the introduction of Treesh’s statements were obtained in violation of his constitutional rights) and 15(c) (he was denied the effective assistance of counsel by trial counsel’s failure to exclude certain jurors), id. at *67-69. We denied Treesh’s request to certify additional claims for appeal.
II. ANALYSIS
A. Standard of Review
We review the district court’s decision to grant or deny a habeas petition de novo. Murphy v. Ohio, 551 F.3d 485, 493 (6th Cir.2009). Because Treesh filed his habeas petition after the effective date of the Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. No. 104-132, 110 Stat. 1214 (“AEDPA”), we may grant the writ “with respect to a ‘claim that was adjudicated on the merits in state court proceedings’ if the state court’s decision ‘was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.’ ” Murphy, 551 F.3d at 493 (quoting § 2254(d)(1)). “A state-court decision is contrary to clearly established federal law ‘if the state court applies a rule that contradicts the governing law set forth in [the Supreme Court’s] cases’ or ‘if the state court confronts a set of facts that are materially indistinguishable from a decision of [the Supreme] Court and nevertheless arrives at a result different from [that] precedent.’ ” Id. at 493-94 (quoting Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). “A state-court decision is an unreasonable ap[429]*429plication of clearly established federal law if it correctly identifies the governing legal rule but applies it unreasonably to the facts of a particular prisoner’s case, or if it either unreasonably extends or unreasonably refuses to extend a legal principle from Supreme Court precedent to a new context.” Id. at 494 (quotation marks and citations omitted).
“[C]learly established Federal law, as determined by the Supreme Court of the United States,” refers to “the holdings, as opposed to the dicta, of [the Supreme] Court’s decisions as of the time of the relevant state-court decision.” Williams, 529 U.S. at 412, 120 S.Ct. 1495. Moreover, “[t]he state court decision need not cite Supreme Court cases, or even evince an awareness of Supreme Court cases, ‘so long as neither the reasoning nor the result of the state-court decision contradicts them.’ ” Williams v. Bagley, 380 F.3d 932, 942 (6th Cir.2004) (quoting Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002) (per curiam)).
B. Miranda Violation
Treesh argues that the trial court admitted statements obtained from him in violation of Miranda. Specifically, he contends that he was never fully apprised of his Miranda rights, he did not knowingly and intelligently waive those rights, his request for counsel was ignored, his statements were not voluntary, and the state court’s conclusions to the contrary were contrary to or involved an unreasonable application of clearly established federal law.
1. Sufficiency of Warnings
In Miranda, the Supreme Court established “certain procedural safeguards that require police to advise criminal suspects of their rights under the Fifth and Fourteenth Amendments before commencing custodial interrogation.” Duckworth v. Eagan, 492 U.S. 195, 201, 109 S.Ct. 2875, 106 L.Ed.2d 166 (1989). In particular, Miranda prescribed the following four warnings:
[A suspect] must be warned prior to any questioning [1] that he has the right to remain silent, [2] that anything he says can be used against him in a court of law, [3] that he has the right to the presence of an attorney, and [4] that if he cannot afford an attorney one will be appointed for him prior to any questioning if he so desires.
Miranda, 384 U.S. at 479, 86 S.Ct. 1602. Although these precise words do not have to be used, “the warnings [must] reasonably convey to a suspect his rights as required by Miranda.” Florida v. Powell, — U.S. -, 130 S.Ct. 1195, 1204, — L.Ed.2d - (2010) (internal quotation marks and alterations omitted).
When Officer Janusczak arrested Treesh around 12:15 a.m. on August 28, 1994, he recited a full set of Miranda warnings. He then asked Treesh if he understood his rights. After Treesh failed to respond, Janusczak began to repeat the warnings, but Treesh interrupted him and said “Yeah, yeah, I know.” The Cleveland Police Department held Treesh in a cruiser at the scene of his arrest until the Euclid Police Department took over custody. Treesh was then transported to the Euclid City Jail, where he showered before being transported to the Eastlake police station around 1:30 to 2:30 a.m. When Treesh arrived at the station, he was immediately taken into a booking room where Lieutenant Doyle gave Treesh the following version of the Miranda warnings:
You understand you’re under arrest? You’ve been arrested before.
Do you understand your Miranda rights? I’m going to ask you some questions over the next hour or so, two [430]*430hours or three hours. You have a right to answer the questions that I ask, or you can stop me at any time. If you can’t afford an attorney, one will be appointed.
Do you understand me? Okay.
According to Doyle, Treesh twice indicated during this interview that he understood his rights. He did not affirmatively request an attorney or invoke his right to remain silent. Instead, Treesh agreed to talk to Doyle and was then interrogated for approximately one hour and forty-five minutes. Sometime during the interview, Doyle asked Treesh if he remembered his rights:
Q: Do you understand your Miranda rights? Okay, I told them to you before, right? Why don’t you tell me.
A: I have the right to remain silent. Anything I say can and will be used against me in a court of law, blase, blase, blase.
Q: You have a right to an attorney. Okay.
After this interview, Treesh was placed in a jail cell, but was awakened shortly before 7:00 a.m. and returned to the booking room. Doyle read the Miranda warnings to Treesh before beginning this interview:
DOYLE: Before we start talking again, just as I told you before, you know your Miranda rights. You know I’m a police officer. You know you’re under arrest, you’re at the police station. I’m going to ask you some questions—
TREESH: — rights before.
DOYLE: Pardon?
TREESH: You gave me the rights before.
DOYLE: Okay, and I plan on continuing doing that. What I have to tell you, though, again, I’m going to ask you questions and you don’t have to answer the questions.
TREESH: Uh-huh.
DOYLE: If you decide to answer the questions, you can stop me at any time. You have a right to an attorney.
TREESH: I already know all my rights.
DOYLE: Okay, but I’m going to tell you them.
TREESH: Okay.
DOYLE: If you can’t afford one, one will be appointed for you. Then I’ve got to say, will you talk to me anyway?
TREESH: Yeah.
DOYLE: Do you understand your rights?
TREESH: Yeah.
Around 7:50 a.m., FBI Special Agent Alford advised Treesh, both orally and in writing, of his Miranda rights. The form Alford gave Treesh included all four required Miranda warnings. Treesh signed the form indicating that he waived those rights. Alford interviewed Treesh for about an hour to an hour and a half. At 10:40 a.m., Doyle interviewed Treesh again. During that interview, he again advised Treesh of his Miranda rights, both orally and in writing, and obtained a written waiver from Treesh. Around 2:00 p.m., Doyle interviewed Treesh and Brooks together. When Doyle told them that the store clerk was alive and had made a statement to police, they requested an attorney. This was Treesh’s first request for an attorney since being arrested.1 Treesh indicated that he would give a [431]*431statement, but only if they assured him they would not seek the death penalty. When Doyle told him they would not make any deals, Treesh refused to give any statements regarding their involvement in the Vine Street News robbery and murder. However, Treesh and Brooks spoke about the involvement of others during the East-lake murder and of crimes committed in other states.
The Ohio Supreme Court concluded that the warnings that Treesh received from Doyle before and during his first interrogation were incomplete. Treesh, 739 N.E.2d at 764-65. Although Treesh testified that Janusczak did not read the Miranda warnings upon his arrest, the Ohio Supreme Court affirmed the trial court’s implicit conclusion that the arresting officer did recite all four Miranda warnings. Id. at 765 (“Though the testimony at the suppression hearing conflicted as to whether the arresting officer actually recited the Miranda warnings, the trial court implicitly found the arresting officer’s testimony about the arrest [to be] more credible than Treesh’s.... We will not substitute our judgment for that of the trial court on this issue.” (internal citation omitted)). Treesh has not presented clear and convicting evidence to indicate that this factual conclusion was erroneous. See James, 470 F.3d at 643.
The Ohio Supreme Court went on to conclude that Janusczak’s “full arrest warning, viewed in conjunction with the partial rewarnings at the interrogations, indicates that Treesh was sufficiently apprised of his Miranda rights.” Treesh, 739 N.E.2d at 765. The question before us, then, is whether the Ohio Supreme Court’s conclusion that Doyle’s incomplete warnings were sufficient to remind Treesh of the previously recited Miranda rights was contrary to or an unreasonable application of clearly established federal law. We hold that it was not.
In reaching its conclusion, the Ohio Supreme Court relied on Wyrick v. Fields, 459 U.S. 42, 103 S.Ct. 394, 74 L.Ed.2d 214 (1982). Treesh, 739 N.E.2d at 764. The Supreme Court in Fields concluded that a suspect did not need to be readvised of his Miranda rights, which he had waived in writing before the initiation of a polygraph examination, because “the circumstances [had not] changed so seriously that his answers no longer were voluntary” and his waiver was still knowing and intelligent. 459 U.S. at 47-48, 103 S.Ct. 394. Since Fields, “[t]he courts have generally rejected a per se rule as to when a suspect must be readvised of his rights after the passage of time or a change in questioners.” United States v. Weekley, 130 F.3d 747, 751 (6th Cir.1997) (concluding that officers did not need to readvise suspect of his Miranda rights where he was read his rights upon his arrest, reminded of his rights during transport and again in the elevator before he was questioned) (internal quotation marks omitted). Instead, we apply a totality-of-the-cireumstances test when considering whether a delay between reading the Miranda warnings and custodial interrogation requires the interrogating officers to readvise the suspect of his Miranda rights. Id. at 751-52.
[432]*432Under Fields, additional warnings are only required if the circumstances seriously changed between the initial warnings and the interrogation. Fields, 459 U.S. at 47, 103 S.Ct. 394. Between Janusczak’s warnings and Doyle’s questioning of Treesh, he was taken first to the Euclid City Jail then to the Eastlake Police Department. However, only approximately two hours had passed between his arrest and his interrogation. Additionally, Doyle partially readvised Treesh of his Miranda rights, which alerted Treesh to the fact that he could still invoke those rights. Treesh’s recitation of at least three of those rights during his interview also demonstrates that he was aware of his rights. Accordingly, the Ohio Supreme Court’s conclusion that Doyle was not required to fully readvise Treesh of his Miranda rights was not contrary to or an unreasonable application of Fields, particularly in light of the application of Fields by our sister circuits. See, e.g., United States v. Clay, 408 F.3d 214, 222 (5th Cir.2005) (no need for rewarning where there was no evidence that suspect no longer understood the warnings or did not understand their applicability to interrogation that occurred two days after initial warning); United States ex rel. Patton v. Thieret, 791 F.2d 543, 547-48 (7th Cir.1986) (Miranda rights did not need to be reread after forty minute lapse); Evans v. McCotter, 790 F.2d 1232, 1237-38 (5th Cir.1986) (rights voluntarily waived where suspect was twice advised of rights over a three-hour period notwithstanding change of interview locations); Stumes v. Solem, 752 F.2d 317, 320 (8th Cir.1985) (five-hour interval between first and second interviews did not invalidate suspect’s waiver given before the first interview); Jarrell v. Balkcom, 735 F.2d 1242, 1254 (11th Cir.1984) (change in interrogators and three-hour lapse did not render confession inadmissible); United States ex rel. Henne v. Fike, 563 F.2d 809, 814 (7th Cir.1977) (nine hours between warnings and waiver not too long).
2. Waiver
Treesh contends that the Ohio Supreme Court’s conclusion that Treesh heard and understood the Miranda warnings recited by Janusczak and that he waived those rights involved unreasonable applications of clearly established federal law. He also argues that the state courts failed to make a determination as to whether Treesh’s waiver was knowing and intelligent. Instead, Treesh contends that the Ohio Supreme Court wrongly consolidated its analysis of the voluntariness of the waiver with its analysis of whether Treesh’s waiver was made knowingly and intelligently. We consider that argument first.
a. Knowing and intelligent waiver
We begin by noting that to the extent Treesh raised this issue before the Ohio Supreme Court, he failed to articulate clearly that he was challenging whether his waiver was knowing and intelligent. Given Treesh’s failure to clearly raise the issue before the Ohio Supreme Court, it is not surprising that the court’s treatment of the issue was not entirely cogent. Nonetheless, the Ohio Supreme Court implicitly concluded that Treesh’s waiver was knowing and intelligent. Although the Ohio Supreme Court never explicitly stated that Treesh made a knowing and intelligent waiver of his rights, it acknowledged that waivers must be knowing and intelligent. Treesh, 739 N.E.2d at 763-64 (“It is well established that a defendant who is subjected to custodial interrogation must be advised of his or her Miranda rights and make a knowing and intelligent waiver of those rights before statements obtained during interrogation will be admissible.”). It also considered factors relevant to that [433]*433analysis. For example, in examining the facts underlying his claim, the court noted that Doyle testified that Treesh did not appear to be under the influence of drugs or alcohol, and that Treesh acknowledged awareness of his rights several times throughout the interviews and eventually signed two written waivers of his rights. Id. at 764-65. The court held that “Treesh was sufficiently apprised of his Miranda rights,” id. at 765, and went on to conclude that “appellant’s waiver was not improperly obtained,” id. at 766.
A suspect may waive his Miranda rights “provided the waiver is made voluntarily, knowingly, and intelligently.” Miranda, 384 U.S. at 444, 86 S.Ct. 1602. “The waiver inquiry ‘has two distinct dimensions.’ ” Berghuis v. Thompkins, 560 U.S. -, 130 S.Ct. 2250, 2260, — L.Ed.2d - (2010) (quoting Moran v. Burbine, 475 U.S. 412, 421, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986)).
First, the relinquishment of the right must have been voluntary in the sense that it was the product of a free and deliberate choice rather than intimidation, coercion, or deception. Second, the waiver must have been made with a full awareness both of the nature of the right being abandoned and the consequences of the decision to abandon it. Only if the “totality of the circumstances surrounding the interrogation” reveal both an uncoerced choice and the requisite level of comprehension may a court properly conclude that the Miranda rights have been waived.
Moran, 475 U.S. at 421, 106 S.Ct. 1135. An express written or oral statement of waiver is not required. North Carolina v. Butler, 441 U.S. 369, 373, 99 S.Ct. 1755, 60 L.Ed.2d 286 (1979). Moreover, although mere silence is not enough to establish a waiver, “silence, coupled with an understanding of his rights and a course of conduct indicating waiver, may [ ] support a conclusion that a defendant has waived his rights.” Id. Thus, “[w]here the prosecution shows that a Miranda warning was given and that it was understood by the accused, an accused’s uncoerced statement establishes an implied waiver of the right to remain silent.” Thompkins, 130 S.Ct. at 2262.
The Ohio Supreme Court’s conclusion that Treesh waived his rights was not an unreasonable application of federal law. When Treesh failed to respond after Janusczak asked Treesh if he understood the rights just read to him, Janusczak began to recite the Miranda warnings again. Treesh interrupted him, however, and said “Yeah, yeah, I know.” He later indicated to Doyle that he understood his rights (admittedly after an incorrect recitation of those rights), and agreed to talk. Additionally, Treesh was able to at least partially recite his Miranda rights. Although he never specifically stated that he waived his rights, such a showing is not required to prove waiver. See id. at 2261. Treesh’s actions indicated that he was aware of his rights and that he waived them. He never invoked his right to counsel or his right to silence. Considering the circumstances, the Ohio Supreme Court’s conclusion that Treesh waived those rights was not an unreasonable application of federal law.
Additionally, the record indicates that the Ohio Supreme Court did not unreasonably apply federal law in concluding that Treesh’s waiver was knowing and intelligent. To be deemed knowing and intelligent, “[t]he Constitution does not require that a criminal suspect know and understand every possible consequence of a waiver of the Fifth Amendment privilege.” Spring, 479 U.S. at 574, 107 S.Ct. 851. Instead, “we examine ‘the particular faets and circumstances surrounding [the] case, including the background, experience, and [434]*434conduct of the accused,’ ” Garner v. Mitchell, 557 F.3d 257, 260 (6th Cir.2009) (alterations in original) (quoting Johnson v. Zerbst, 304 U.S. 458, 464, 58 S.Ct. 1019, 82 L.Ed. 1461 (1938)), to determine “whether the ‘suspect [knew] that he [could] choose not to talk to law enforcement officers, to talk only with counsel present, or to discontinue talking at any time,’ ” id. (alterations in original) (quoting Spring, 479 U.S. at 574, 107 S.Ct. 851). “[T]he Supreme Court has never said that impairments from drugs, alcohol, or other similar substances can negatively impact” a suspect’s waiver of his Miranda rights. Matylinsky v. Budge, 577 F.3d 1083, 1095 (9th Cir. 2009).
The evidence supports the Ohio Supreme Court’s implicit conclusion that Treesh knowingly and intelligently waived his rights. He appears to have understood the rights Janusczak read to him, evidenced by his interrupting Janusczak’s second recitation of those rights and saying “Yeah, yeah, I know.”2 Additionally, he continuously told officers who interrogated him that his rights had been read to him and was even able to partially recite those rights. Moreover, every officer who interrogated Treesh testified that he appeared to be coherent, was not confused or disoriented by the questions they asked, and did not appear to be under the influence of drugs or alcohol. In further support of the conclusion that Treesh made a knowing and intelligent waiver of his rights, Treesh ultimately signed a written waiver. Treesh later testified that he was familiar with the criminal justice system, that he knew his rights, and that he knew where he was when he arrived at the Eastlake Police Station. Given the officer’s testimony regarding Treesh’s mental state, as well as Treesh’s statements to police and other indications that he understood his rights, it was not unreasonable for the Ohio Supreme Court to conclude that Treesh knowingly and intelligently waived his Miranda rights.
b. Voluntariness of the waiver
In his brief, Treesh contends that “even if [he] had been properly warned of and had knowingly waived his Miranda rights, his statements were not voluntary,” because he “was coerced into confessing when Officer Doyle lied to him by falsely claiming that a video tape of the crime existed, and by exploiting Treesh’s desire to exonerate his girl friend.” Treesh also argues that the officers were “overreaching” by exploiting Treesh’s exhaustion and cocaine-induced high. Nonetheless, he cites no case law in support of his argument.
“[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.’ ” United States v. Elder, 90 F.3d 1110, 1118 (6th Cir.1996) (quoting United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990)); see also United States v. Layne, 192 F.3d 556, 566-67 (6th Cir.1999) (deeming issue waived where defendant did not make a legal argument regarding the issue). Because Treesh has not developed a legal argument regarding the vol[435]*435untariness of his statement, he has forfeited this issue on appeal.
C. Ineffective Assistance of Counsel
Treesh asserts that he was denied the effective assistance of counsel when trial counsel failed to challenge jurors Cynthia Barth and Barbara Módica for cause. Cynthia Barth took paralegal classes taught by the prosecutor in this case, Charles Coulson. The trial judge asked Barth whether “[t]he fact that [Coulson] was [her] instructor[ ] would ... put [her] in a position that [she] could not listen to the case and render a fair and impartial verdict?” Barth responded that it would not. Coulson followed up on the issue with the following exchange:
Coulson: Mrs. Barth, I see you are a paralegal. Did I help you get there?
Barth: Yes.
Coulson: Do you think your experience as a paralegal would in any way interfere with your ability to listen to the law as the Judge gives it to you and apply it in this case?
Barth: No, I think it would help actually-
Coulson: You think you might be able to understand these instructions even better?
Barth: Hopefully.
Coulson: Well if I did any good, I hope so. I had you for research and writing?
Barth: Yes.
Coulson: I think you mentioned that.
Barth: Actually I think that your paralegal was there more than you were. I didn’t mean to embarrass you.
Treesh’s trial counsel did not ask Barth any questions about her relationship with Coulson. Counsel passed for cause and Barth was seated as a juror.
During voir dire, Módica admitted that she had seen media reports about the case and made statements suggesting that she was predisposed in favor of the death penalty. Módica stated that she had read three to four articles about the case in the Cleveland Plain Dealer, that she “followed” the case, found it interesting, had discussed the case with friends (but not at great length), and that she would presume the articles were “pretty much accurate.” However, she noted that she did not believe everything she read in the newspaper. Módica also stated that she would be able to ignore what she read and decide the case based on the evidence presented in the courtroom. Treesh’s counsel did not follow-up regarding Modica’s exposure to the case. In response to her statement that she believed in the death penalty, however, Treesh’s counsel had the following exchange with Módica:
Hawkins: You indicated to both the Judge and the Prosecutor that you favor the death penalty, that correct?
Módica: When it’s warranted.... It seems to me that if someone is judged guilty of a crime that’s heinous enough to even bring that charge against him, if he’s guilty I don’t see even why he should be up and walking around.
Hawkins: Now, you said heinous crime, what crimes did you have in mind when you said that?
Módica: Well, murder is what I am thinking.
Hawkins: Do you think anybody that purposely kills another, purposely murders another themselves should be put to death?
Módica: No.... If it was something happens that wasn’t planned ahead of time, or — I don’t know exactly.... I am thinking maybe if you did it out of [436]*436a moment of instant passion, or something like that.
Nonetheless, Módica also mentioned several factors that would impact her decision regarding the death penalty, including a person’s reasons for committing murder, whether he was mentally retarded or had developmental difficulties, and whether he was under the influence of drugs. She also stated that she would be able to make a decision based on the evidence presented and apply the law as directed by the judge. Treesh’s counsel passed for cause as to Módica and she was seated as a juror.
1. Legal Standard
We engage in a two-part inquiry when reviewing ineffective-assistance-of-counsel claims:
First, the defendant must show that counsel’s performance was deficient. This requires showing that counsel made errors so serious that counsel was not functioning as the “counsel” guaranteed the defendant by the Sixth Amendment. Second the defendant must show that the deficient performance prejudiced the defense. This requires a showing that counsel’s errors were so serious as to deprive the defendant of a fair trial, a trial whose result is reliable.
Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). We are not required to “address both components of the inquiry if the defendant makes an insufficient showing on one.” Id. at 697, 104 S.Ct. 2052. For example, we “need not determine whether counsel’s performance was deficient before examining the prejudice suffered by the defendant as a result of the alleged deficiencies.” Id. Because “it is easier to dispose of [Treesh’s] ineffectiveness claim on the ground of lack of sufficient prejudice,” we do not determine whether trial counsel’s performance was deficient. Id.
Treesh asserts that no state court evaluated the prejudice prong of Strickland, and that we should therefore not apply AEDPA deference to that prong. We disagree. In discussing the controlling law for ineffective assistance of counsel claims, the Ohio Supreme Court cited the appropriate prejudice standard under Strickland. Treesh, 739 N.E.2d at 778. In rejecting the specific claims at issue here, it explained as follows:
Treesh contends that his counsel were ineffective for failing to challenge two jurors, Cynthia Barth and Barbara Módica, during voir dire. Treesh argues that counsel should have challenged Barth because she had taken paralegal classes taught by the prosecutor, Charles Coulson. Treesh claims that counsel should have challenged juror Módica due to her media exposure about the case and her alleged predisposition in favor of the death penalty. We find both contentions meritless. It is unlikely that a challenge for cause, if made, would have succeeded in either case. Barth testified that her past affiliation with Coulson’s paralegal course would not impair her ability to render a fair and impartial verdict. Likewise, though Módica admitted exposure to some newspaper articles about the case, and admitted that she favored the death penalty “[w]hen it’s warranted,” she stated that she had not formed an opinion about the case and that she could fairly and impartially weigh the evidence presented.
Id. at 779. Although the Ohio Supreme Court did not use the word “prejudice” in this particular discussion, it is clear that its conclusion was based on the prejudice prong. The court reasoned that “[i]t is unlikely that a challenge for cause, if made, would have succeeded in either case.” Id. This clearly entails an adjudica[437]*437tion on prejudice grounds. However, because the court did not set out the general juror-bias standard in discussing whether trial counsel’s failure to challenge the jurors for cause was prejudicial, we review the claim through AEDPA’s contrary-to clause. Packer, 537 U.S. at 8, 123 S.Ct. 362 (explaining that where the state court does not cite federal law, we may only grant habeas “so long as neither the reasoning nor the result of the state-court decision contradicts [federal law]”).
To establish prejudice, Treesh “must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Strickland, 466 U.S. at 694, 104 S.Ct. 2052. Strickland defined “reasonable probability” as “a probability sufficient to undermine confidence in the outcome.” Id. To show prejudice arising out of trial counsel’s failure to challenge a juror, however, Treesh must show that the juror was biased against him. Johnson v. Luoma, 425 F.3d 318, 328 (6th Cir.2005). If a biased juror was impaneled, “prejudice under Strickland is presumed, and a new trial is required.” Hughes v. United States, 258 F.3d 453, 463 (6th Cir.2001).
Bias may be actual or implied. See Johnson, 425 F.3d at 326. “Actual bias is ‘bias in fact’ — the existence of a state of mind that leads to an inference that the person will not act with entire impartiality.” Hughes, 258 F.3d at 463 (citation and internal quotation marks omitted). “The doctrine of presumed or implied, as opposed to actual, bias provides that, in certain ‘extreme’ or ‘exceptional’ cases, courts should employ a conclusive presumption that a juror is biased.” Johnson, 425 F.3d at 326 (quoting United States v. Frost, 125 F.3d 346, 379 (6th Cir.1997)). We may presume bias “only where the relationship between a prospective juror and some aspect of the litigation is such that it is highly unlikely that the average person could remain impartial in his deliberations under the circumstances.” Id. (internál quotation marks and citation omitted). Examples of such a relationship are “that the juror is an actual employee of the prosecuting agency, that the juror is a close relative of one of the participants in the trial or the criminal transaction, or that the juror was a witness or somehow involved in the criminal transaction.” Smith v. Phillips, 455 U.S. 209, 222, 102 S.Ct. 940, 71 L.Ed.2d 78 (1982) (O’Connor, J., concurring).
2. Cynthia Barth
Treesh asserts that we may presume that Barth was biased against him based on her student-teacher relationship with Coulson, and that she was actually biased. First, as to implied bias, we have previously expressed doubt over the continued viability of the doctrine of implied bias after Smith. See Johnson, 425 F.3d at 326 (“Courts that have reviewed the Smith decision, including this circuit, have suggested that the majority’s treatment of the issue of implied juror bias calls into question the continued vitality of the doctrine.”). Nonetheless, even accepting its continued viability, there is no Supreme Court precedent recognizing implied bias from a mere student-teacher relationship. Although Coulson was the instructor for Barth’s research and writing course, Barth stated that she thought his “paralegal was there more than” he was. There is nothing in the record that indicates that Coulson’s and Barth’s relationship rose to the level of the sort of extreme or exceptional case where bias is conclusively presumed. Thus, the Ohio Supreme Court’s failure to find implied bias was not contrary to clearly established federal law.
[438]*438Additionally, the record does not establish actual bias. Barth and Coulson did not appear to have had a close relationship. Barth also indicated that Coulson’s status as her former instructor would not put her in a position such that she “could not listen to. the case and render a fair and impartial verdict.” Finally, she swore “to well and truly try the issue joined between the parties in this case and a true verdict enter according to the evidence.” Considering Barth’s ability to promise to be impartial and the lack of evidence in the record indicating she was actually biased, we agree with the Ohio Supreme Court’s conclusion that a challenge for cause against Barth would have most likely been unsuccessful. Without actual or implied bias, Treesh cannot demonstrate prejudice from the seating of Barth.
3. Barbara Módica
Treesh asserts that Módica was actually biased against Treesh, given her predisposition in favor of the death penalty and her prior exposure to media coverage of the case. “[I]t is beyond question that mere prior knowledge of the existence of the case, or familiarity with the issues involved, or even some preexisting opinion as to the merits, does not in and of itself raise a presumption of jury taint.” DeLisle v. Rivers, 161 F.3d 370, 382 (6th Cir.1998) (en banc). “Where pretrial publicity cannot be presumed prejudicial, [we] must then determine whether it rises to the level of actual prejudice.” Foley v. Parker, 488 F.3d 377, 387 (6th Cir.2007). To assess actual prejudice, we review the voir dire of prospective jurors. Id. “The relevant question is ‘did [the] juror swear that [she] could set aside any opinion [she] might hold and decide the case on the evidence, and should the juror’s protestation of impartiality have been believed.’” Id. (quoting Patton v. Yount, 467 U.S. 1025, 1036, 104 S.Ct. 2885, 81 L.Ed.2d 847 (1984)). Módica swore she could set aside any prior opinion, and nothing in the record indicates that her prior exposure to the case via media coverage undermined her promise to be impartial.
Similarly, Modica’s statements regarding the death penalty do not demonstrate actual bias. “[A] prospective juror may be excluded for cause because of his or her views on capital punishment ... [when] the juror’s views would ‘prevent or substantially impair the performance of [her] duties as a juror in accordance with [her] instructions and [her] oath.’ ” Wainwright v. Witt, 469 U.S. 412, 424, 105 S.Ct. 844, 83 L.Ed.2d 841 (1985) (quoting Adams v. Texas, 448 U.S. 38, 100 S.Ct. 2521, 65 L.Ed.2d 581 (1980)). “A juror who will automatically vote for the death penalty in every case will fail in good faith to consider the evidence of aggravating and mitigating circumstances as the instructions require [her] to do.” Morgan v. Illinois, 504 U.S. 719, 729, 112 S.Ct. 2222, 119 L.Ed.2d 492 (1992). Nonetheless, after carefully reviewing the record, there is nothing to indicate that Modica’s views on the death penalty would have prevented her from returning anything less than a death sentence. It is true that Módica initially indicated that she thought that anyone guilty of murder should not be “up and walking around.” However, when pressed to consider the issue further, she admitted that she did not believe that everyone who purposely murdered should be sentenced to death. She explained that such a sentence may not be warranted when the murder was the result of momentary passion, and indicated that she would consider factors such as why the defendant committed the murder, what the circumstances were, whether the defendant was mentally retarded or had developmental difficulties as a child, and whether he was using drugs at the time. These statements suggest that [439]*439Módica would not “automatically vote for the death penalty in every case,” and demonstrate that she could take into consideration mitigating factors. Accordingly, the Ohio Supreme Court’s conclusion that it was unlikely that Módica would have been excluded pursuant to a challenge for cause is not contrary to clearly established Supreme Court precedent.
D. Certificate of Appealability
Treesh also argues that he is entitled to a COA on his claim that lethal injection as conducted in Ohio violates the Eighth Amendment. Under AEDPA, an appeal from the denial of a writ of habeas corpus may not be taken unless a COA has been issued. 28 U.S.C. § 2253(c)(1). A COA may not issue unless “the applicant has made a substantial showing of the denial of a constitutional right.” § 2253(c)(2). We decline to expand Treesh’s COA, because he has not “made a substantial showing of the denial of a constitutional right.” See Cooey (Biros) v. Strickland, 589 F.3d 210 (6th Cir.2009).
III. CONCLUSION
For the foregoing reasons, we AFFIRM the district court’s denial of Treesh’s petition.