OPINION
BOGGS, Circuit Judge.Gary Otte is an Ohio prisoner on death row. He appeals the district court’s denial of his petition for a writ of habeas corpus, which was filed pursuant to 28 U.S.C. § 2254. A certificate of appealability was issued for three claims: 1) whether Otte’s waiver of his right to a jury trial was voluntary, knowing, and intelligent; 2) whether Otte’s counsel provided ineffective assistance at the penalty phase of his case; and 3) whether Otte’s confession should have been suppressed because the waiver of his rights under Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), was invalid. We affirm the district court’s decision to deny the petition.
I
In September 1992, a three-judge panel found Otte guilty of the murders of Sharon Kostura and Robert Wasikowski. The Ohio Supreme Court summarized the facts:
On February 11, 1992, Otte stole his grandfather’s red 1962 Chevrolet Impala and .22 revolver and left Terre Haute, Indiana. He also stole two credit cards belonging to his uncle and aunt. Otte arrived in Parma, Ohio, the next day and tried to use the stolen cards in local stores, but they were confiscated.
*597Otte next drove to see his Mend Mike Carroll (“Carroll”)- Carroll lived with his fiancee and Jerry “J.J.” Cline (“J.J.”) in the Pleasant Lake apartment complex in Parma.
After that Otte drove to Gypsy and Rob’s, a Cleveland bar, where he found J.J. Otte asked J.J. “if he was still robbing people.” J.J. said he planned to “hit” two people at Pleasant Lake. One was a woman in her thirties with a Visa gold card; she lived alone “one building over” from J.J. and Carroll. The other was “an old man that lives diagonally from [Carroll’s] apartment that is a drunk and has lots of money.”
That evening, Otte returned to Pleasant Lake alone. He went to Carroll’s apartment, but nobody was home. He then knocked on the door of Mary Ann Campangna (“Campangna”), who lived next to Carroll and across the hall from Robert Wasikowski. Otte claimed his car had overheated, said he was looking for Carroll, and asked for oil. Campangna told him she didn’t have any, and Otte left.
Otte saw Wasikowski drive into the parking lot and thought that “that was the man” J.J. had described. Otte came out and asked Wasikowski for some oil, telling him the same story about his car overheating. As they spoke, Otte noticed that Wasikowski had been drinking. Wasikowski drove Otte to a gas station to buy oil.
When they returned, Otte asked to use Wasikowski’s phone; after some hesitation, Wasikowski agreed. Otte followed Wasikowski into his apartment. Looking through her peephole, Campangna found this “very strange,” so she continued to watch Wasikowski’s door. Six or seven minutes later, Campangna heard “a very loud crack, cracking sound.”
Inside the apartment, Otte pretended to make a phone call, then “tried to stall for time.” Finally, Wasikowski asked Otte to leave. Otte went to the door, opened it, then slammed it shut and drew a gun. Wasikowski offered Otte $10 from his pocket. Otte pulled the trigger anyway, but the gun wouldn’t fire. Wasikowski asked, “[I]t isn’t loaded, is it[?]” Otte then fired the gun at Wasikowski’s head. This time, it went off. Wasikowski fell to the floor, gasping and begging for help. Otte found this “the most horrible sight that I have ever seen”; nonetheless, he turned up the volume on the TV and went through Wasikowski’s pants pocket, took out his wallet and took his cash, about $413. Otte searched for more money, but found only some fifty-cent pieces in the bedroom. He considered shooting himself, “but something told me not to,” so he stole the fifty-cent pieces and left through the sliding glass patio door.
Otte then returned to Gypsy and Rob’s, where he paid an $80 debt, played pool, drank, and took drugs. At 2:30 a.m., he left the bar, but continued to “party” until 10:00 or 10:30 a.m., when he checked into a hotel and slept until 5:00 p.m.
When Wasikowski failed to report for work on February 13, his employer called the Parma police. An officer entered the apartment and found Wasikowski dead. Robert Challener, the chief deputy county coroner, later performed an autopsy. He found that Wasikowski died from a gunshot to the head fired from less than two feet away.
Meanwhile, Parma police investigated the murder. Capt. Joseph Bistricky (“Bistricky”) interviewed Mary Ann Campangna, who described the man she had seen as “a white male, early 20’s, six feet, thin to medium build, with blond*598ish-brown hair, and a mustache.” She suggestéd that Mike Carroll might know him.
Around 1:30 p.m., Bistricky interviewed Carroll, who said he knew the person Campangna had seen; his name was Gary, he was from Indiana, and he was driving his grandfather’s car, a red 1962 Impala in good condition. Carroll’s description of “Gary” matched Campangna’s. Carroll promised to call police if he found out more about Gary’s identity or location. Later that day Carroll told the police Gary would be at Gypsy and Rob’s around 7:30 p.m.
On the evening of February 13, Otte went back to Pleasant Lake to rob Sharon Kostura. Otte knocked on her door; when she answered, he drew a .22 revolver and shoved his way in. He closed and locked the door. Kostura screamed and Otte shot her in the head. He stole about $45 from her purse, took her car keys and checkbook, and left through the patio door. Police later found Otte’s fingerprint on that door.
After dinner, Otte returned to Gypsy and Rob’s. He left with Carroll, J.J., and someone known as “Buster.” They “smoked dope” in the Impala, then visited someone called “Patty.” After leaving Patty’s house, Otte dropped off J.J. and Buster near the bar.
Otte then drove past several police officers near Gypsy and Rob’s. Because Carroll had told Capt. Bistricky that Otte would be at the bar that night, the officers were waiting for Otte. They pulled him over and ordered him to shut off the engine and throw out the keys. Carroll told the officers, “The guns are in the trunk.” Officers opened the trunk and found a .22 caliber revolver and a .25 caliber semi-automatic pistol. The officers began an inventory search of the car but because of bad weather and a gathering crowd, Bistricky ordered the car towed, and the search was completed at the police garage.
In the glove compartment, police found Kostura’s checkbook, a set of Hyundai car keys, and a box of .22 caliber live shells. In the passenger compartment, they found ammunition for the .25 caliber gun and a pillow with a red stain. A detective documented the items found on an inventory form.
Because Kostura had not reported her checkbook stolen, officers went to her apartment, where they found her still alive. Kostura was taken to the hospital and lived eight days, until February 21. Dr.. Challener found that the gunshot wound to her head killed her.
Det. John Bomba interrogated Otte within an hour of his arrest on February 13. Otte denied going to the Pleasant Lake Apartments on February 12 or 13. He claimed he had no idea how Kostura’s checkbook got into the car and “never even saw the guns until the police said they were in the trunk.”
On the afternoon of February 14, Det. Robert DeSimone interrogated Otte. Otte confessed to shooting and robbing Wasikowski and Kostura. On February 16, Otte signed a confession. On February 20, Otte asked to speak with DeSimone; he corrected part of his February 16 statement and answered questions.
State v. Otte, 74 Ohio St.3d 555, 660 N.E.2d 711, 715-16 (1996).
Otte was indicted for aggravated murder as to each victim. He filed a motion to suppress his confession, but it was denied after a hearing. After waiving his right to a jury trial, Otte was tried and convicted by a three-judge panel. At the penalty phase, Otte presented Dr. Sandra McPherson, who testified about Otte’s childhood troubles fitting in, his depression and early drug use, as well as his success within very *599structured environments. Otte’s parents also gave testimony about their son’s troubles growing up, and Otte himself gave an unsworn statement. After considering this mitigation evidence, the panel nonetheless imposed a death sentence.
Otte filed a timely direct appeal to the Eighth District Court of Appeals, which affirmed the trial court’s convictions and death sentence. State v. Otte, No. 64617, 1994 WL 590556 (Ohio Ct.App. Oct. 27, 1994). Otte appealed that decision to the Ohio Supreme Court, which also affirmed. Otte, 660 N.E.2d 711. He next filed a petition for a writ of certiorari with the United States Supreme Court, but it was denied in October 1996. Otte v. Ohio, 519 U.S. 836, 117 S.Ct. 109, 136 L.Ed.2d 62 (1996). While his appeals were pending, Otte also sought post-conviction relief in the Ohio trial court, in which he raised all of the claims now before us. The post-conviction court denied relief and Otte appealed in July 1999. The Eighth District Court of Appeals eventually remanded in part for the trial court to conduct an evidentiary hearing on some of Otte’s claims. State v. Otte, No. 76726, 2001 WL 69139 (Ohio Ct.App. Jan. 25, 2001). At the hearing, new evidence was presented with regard to the claims now before us. Nonetheless, the trial court once again denied relief and the Eighth District Court of Appeals affirmed in January 2005. State v. Otte, No. 84455, 2005 WL 77071 (Ohio Ct.App. Jan. 13, 2005). The Ohio Supreme Court declined to hear the case, State v. Otte, 106 Ohio St.3d 1461, 830 N.E.2d 1169 (2005), and the United States Supreme Court denied Otte’s petition for a writ of certiorari, Otte v. Ohio, 546 U.S. 1099, 126 S.Ct. 1031, 163 L.Ed.2d 870 (2006).
Having exhausted his state court remedies, Otte next sought a writ of habeas corpus from the federal district court. The district court denied the petition, Otte v. Houk, No. 1:06CV1698, 2008 WL 408525 (N.D.Ohio Feb. 12, 2008), but a certificate of appealability was granted for the three issues before us: 1) whether Otte’s waiver of his right to a jury trial was voluntary, knowing, and intelligent; 2) whether Otte’s counsel provided ineffective assistance during the penalty phase; and 3) whether Otte’s confession should have been suppressed because his Miranda waiver was invalid. All of these claims were adjudicated on the merits in state court. We now affirm.
II
“We review a district court’s denial of a petition for writ of habeas corpus de novo.” Tibbetts v. Bradshaw, 633 F.3d 436, 441 (6th Cir.2011). Because Otte filed this petition after the effective date of the Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”), we are bound by its strictures. We may not grant habeas relief on any claim that was adjudicated on the merits in state court unless the adjudication:
(1) 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 States; or
(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d). A decision is “contrary to” clearly established federal law when “the state court arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law or if the state court decides a case differently than [the Supreme] Court has on a set of materially indistinguishable facts.” Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court’s adjudication only results in an “un*600reasonable application” of clearly established federal law when “the state court identifies the correct governing legal principle from [the Supreme] Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case.” Id. at 413, 120 S.Ct. 1495. This is a difficult standard for any petitioner to meet. Indeed, the Supreme Court has been increasingly vigorous in enforcing AEDPA’s standards. See, e.g., Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011) (holding that AEDPA limits a federal habeas court to the record before the state court where a claim has been adjudicated on the merits by the state court). It is not enough for us to determine that the state court’s determination is incorrect; to grant the writ under this clause, we must hold that the state court’s determination is unreasonable. Schriro v. Landrigan, 550 U.S. 465, 473, 127 S.Ct. 1933, 167 L.Ed.2d 836 (2007). This is a “substantially higher threshold.” Ibid. To warrant AEDPA deference, a state court’s “decision on the merits” does not have to give any explanation for its result, Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 784, 178 L.Ed.2d 624 (2011), nor does it need to cite the relevant Supreme Court cases, as long as “neither the reasoning nor the result of the state-court decision contradicts them,” Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002) (per curiam). In addition, the state court’s findings of fact are presumed correct and can be rebutted only when the petitioner presents clear and convincing evidence to the contrary. 28 U.S.C. § 2254(e)(1).
In deciding whether a state’s decision is contrary to or an unreasonable application of Supreme Court precedent, we look to Supreme Court cases already decided at the time the state court made its decision. Lockyer v. Andrade, 538 U.S. 63, 71-72, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003). We look to our own decisions “to the extent [they] have already reviewed and interpreted the relevant Supreme Court case law to determine whether a legal principle or right had been clearly established by the Supreme Court.” Landrum v. Mitchell, 625 F.3d 905, 914 (6th Cir.2010) (alterations in original).
A. Jury waiver
In his first claim for relief, Otte argues that he could not make a voluntary, knowing, and intelligent waiver of his right to a jury trial because the jail doctor put him on the drug Mellaril. Mellaril is an anti-psychotic medication, but it was given to Otte to help him sleep. At the state’s post-conviction evidentiary hearing, Otte presented the expert testimony of pharmacologist Dr. Richard Nockowitz, who opined that Otte was suffering side effects from Mellaril that would have left him without the cognitive capacity to waive his rights. Otte’s mother also testified that one of Otte’s two attorneys (who was deceased by the post-conviction hearing) told her that Otte had not wanted to waive the jury trial. The state called Dr. McPherson, who testified that she had not been concerned about Otte’s capacity, as well as Dr. Shin Lee, the prescribing physician, who testified that Otte was oriented to the “three spheres” of time, place, and the person to whom he was speaking. The state also called psychiatrist Dr. Phillip Resnick, who testified that there was no indication that Otte was incompetent at the time of his waiver.
Because the right to a jury trial is fundamental, a waiver of that right must be voluntary, knowing, and intelligent. Haliym v. Mitchell, 492 F.3d 680, 698 (6th Cir.2007) (citing Duncan v. Louisiana, 391 U.S. 145, 149, 88 S.Ct. 1444, 20 L.Ed.2d 491 (1968); Brady v. United States, 397 U.S. 742, 748, 90 S.Ct. 1463, 25 L.Ed.2d *601747 (1970)). A petitioner bears the burden of proving that his waiver was not, in fact, voluntary, knowing, and intelligent. Ibid. A colloquy between the court and the defendant is not constitutionally required, although it is advised. Ibid. “[T]he dispositive inquiry is whether the defendant understood that the choice confronting him was, on the one hand, to be judged by a group of people from the community, and on the other hand, to have his guilt or innocence determined by a judge.” Jells v. Mitchell, 538 F.3d 478, 510 (6th Cir.2008) (internal quotation marks omitted).
The Ohio Court of Appeals, after reviewing the above testimony adduced at the post-conviction evidentiary hearing, held for the state. The court appeared to credit Dr. Resnick’s conclusion that it was significant that Otte was able to testify coherently and in great detail at a suppression hearing held on the same day that he waived his right to a jury trial. The court also noted that Dr. Resnick was a qualified expert, and that the trial court had exercised its discretion to credit his testimony over Dr. Nockowitz’s. Otte now claims that these factual determinations were unreasonable in light of Dr. Nockowitz’s testimony.
We cannot agree. Dr. Nockowitz stated that Otte suffered from the side-effect of akathisia, a condition characterized by restlessness and anxiety. He stated that Mellaril can block acetylcholine, thereby causing delirium and confusion. He cited Otte’s constipation as evidence that he was suffering from the side effects of Mellaril. However, after reviewing Otte’s records, Dr. Resnick disagreed with that diagnosis. In his opinion, Otte’s clear and articulate testimony at the suppression hearing showed that, although Mellaril can cause cognitive side effects, there was no evidence that Otte was actually suffering from any impairment to such a degree that his waiver would be invalid. Otte’s restlessness, he opined, was not caused by the medication, because he had exploded in a violent rage several days before beginning the treatment. Dr. Resnick also testified that in his experience prescribing Mellaril to his patients, it was possible that Otte could have suffered some of the side effects (such as constipation) without experiencing all of them (such as cognitive impairment). It appears that both experts were well qualified to give testimony and butted heads over largely overlapping issues. Even if we were to believe Dr. Nockowitz’s testimony, Otte has failed to show that the state court’s factual determination was unreasonable. “For a federal habeas court to overturn a state court’s credibility judgments, the state court’s error must be stark and clear.” Larry v. Branker, 552 F.3d 356, 370 (4th Cir.2009). This is not such a case.
B. Ineffective assistance of counsel
Not every bad lawyer violates the Constitution. For counsel’s performance to be deemed ineffective, it must be objectively deficient and cause prejudice to the defendant. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). To establish prejudice, “[t]he defendant must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different. A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. at 694, 104 S.Ct. 2052.
In his second claim, Otte argues that his counsel provided constitutionally ineffective assistance during mitigation. This claim is divided into two subparts: 1) counsel were ineffective for failing to request a substance abuse expert; 2) counsel *602were ineffective for failing to present mitigating evidence from Otte’s upbringing.
1. Substance abuse expert
Otte argues that his counsel were ineffective for failing to retain a substance abuse expert who could testify as to Otte’s alcohol, cannabis, and cocaine dependence. In the state’s post-conviction evidentiary hearing, Otte presented the testimony of Dr. Smith, who was just such an expert. Dr. Smith testified that people under the influence are more likely to be impulsive and make bad decisions. Otte claims that someone like Dr. Smith could have “put these uncharacteristic acts into context and given the sentencing panel some explanation for the offenses.” Appellant’s Br. 57.
As a general matter, counsel’s failure to make a reasonable investigation of a defendant’s history and present this evidence at mitigation can constitute ineffective assistance. Wiggins v. Smith, 539 U.S. 510, 522-23, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003). Otte points to no case, however, in which the failure to retain a substance abuse expert has been grounds for granting habeas relief. As the Wiggins court noted, “Strickland does not require counsel to investigate every conceivable line of mitigating evidence no matter how unlikely the effort would be to assist the defendant at sentencing.” Id. at 533, 123 S.Ct. 2527. After reviewing Dr. Smith’s testimony, the Ohio Court of Appeals held that Otte was not prejudiced by the lack of a substance abuse expert because evidence of his long history of drug abuse was introduced by Dr. McPherson and Ohio law gives little weight to alcoholism and drug addiction in sentencing.
We have rejected many claims of this type before. In Clark v. Mitchell, 425 F.3d 270 (6th Cir.2005), the petitioner’s counsel called an expert at mitigation who testified that Clark was a drug addict and his “need for drug money had a contributing effect to Clark’s crimes.” 425 F.3d at 275. Before this court, Clark argued that his counsel should have retained a pharmacologist who could have testified in greater detail as to the effects of his drug addiction. We refused to find the state court’s decision unreasonable because the expert actually called at mitigation “addressed Clark’s drug addiction and its effect on his criminal conduct.” Id. at 285. In White v. Mitchell, 431 F.3d 517, 530 (6th Cir.2005), we rejected an ineffective assistance claim de novo that was premised on counsel’s failure to retain “experts to explain the effect of intoxication on White at the time of the crime.” In that case, we held that the evidence would have been cumulative because the jury was aware that White had been drinking and another expert testified about the effects of alcohol on White’s mood and behavior. Most recently, in Tibbetts, 633 F.3d at 443, we rejected the petitioner’s argument of ineffective assistance for failure to present a pharmacologist because the expert who actually testified mentioned that “Tibbetts’ use of drugs and alcohol was an explosion waiting to happen, and that Tibbetts was unable to control his rage response while intoxicated.”
Otte’s case is not meaningfully distinguishable from these. During the penalty phase, Dr. McPherson testified as to Otte’s drug and alcohol dependence from a young age, as well as the effects that drug and alcohol use might have had on him. She stated that Otte’s life was “primarily related around the use of drugs and alcohol----Periodically people support themselves in this kind of situation, not only by acts of theft or anti-social behavior, but they also sell drugs to get money.” She also testified that Otte “had a pretty heavy crack cocaine habit, which are [sic] not *603only expensive, but also extremely damaging as to how they [a]ffect psychological functioning.” She testified that “the first thing that the alcohol drugs [sic] knock out is the control system.” She also gave her opinion that the drugs and alcohol made Otte more likely to commit crimes. (“If he is clean, sober, he is not likely to do this.”). It was very well established that Otte had been drinking and consuming drugs around the time of the murders. Considering the entirety of Dr. McPherson’s testimony, then, we do not see how a substance abuse expert could have affected the panel’s decision to impose a death sentence. Because such testimony would have been largely cumulative, Otte cannot establish that he was prejudiced, and this claim fails.
2. Other evidence of Otte’s upbringing
Otte also argues that his counsel were constitutionally ineffective for failing to present witnesses as to Otte’s upbringing. Otte’s attorneys, Patrick D’Angelo and Granville Bradley, hired mitigation specialist Pat Snyder to investigate Otte’s history. Snyder traveled to Otte’s childhood home of Terre Haute, Indiana, where she identified a number of people who might testify on Otte’s behalf. On appeal, Otte points specifically to three witnesses. Sharon Joslin was Otte’s second- and fifth-grade teacher, and described him as a “very sad little boy” who had trouble fitting in. Julia Bonham was Otte’s fourth-grade teacher; she echoed Joslin’s recollection that Otte had trouble being accepted by the other children. Bonham stated that even though Otte was frequently bullied, he did not fight back. Finally, Katherine Hoffman was a drug-program administrator who could have testified about Otte’s trouble fitting in with his family and his success at the Gibault School, a structured detention facility for children. Otte also argues that his counsel were constitutionally ineffective by failing to present his school records, which indicated that Otte did very poorly and was referred for psychological testing, and which contained a notation that Otte was “seriously emotionally handicapped.”
The Ohio Court of Appeals rejected this claim based largely on the post-conviction testimony of Otte’s lead attorney, D’Angelo, who claimed that he made a tactical decision not to use these materials because they were a “double-edged sword.” In his words, “you can try to make a sympathetic case, but at the same time it cuts the other way because it shows someone that’s kind of cold blooded and getting worse and dangerous and people were predicting certain things and, lo[ ] and behold, look what happened here.” After considering this testimony, the Ohio Court of Appeals held that counsels’ tactical decision not to use the Snyder materials was not unreasonable.
Strickland warns that “strategic choices made after thorough investigation of law and facts relevant to plausible options are virtually unchallengeable,” 466 U.S. at 690, 104 S.Ct. 2052, and D’Angelo was adamant that his mitigation choices were indeed strategic. He testified that he looked over the Snyder materials, discussed them with Snyder, and ultimately decided that they would not be helpful. Otte seeks to show that the state court’s decision to credit D’Angelo’s testimony was an unreasonable determination of the facts. Although Otte points to a number of inconsistencies in D’Angelo’s testimony, this is hardly surprising considering that more than ten years separated Otte’s trial and the post-conviction hearing. Further, D’Angelo’s testimony freely admits his limited recollection of many aspects of the case, but becomes very lucid with regard to his struggle deciding whether to use the Snyder materials. Thus, we cannot say that *604D’Angelo’s misstatements render the state court’s decision to credit his testimony an unreasonable determination of the facts.
It was also reasonable for the state court to credit D’Angelo’s stated rationale for declining to present the Terre Haute witnesses. D’Angelo claimed that the information presented could have hurt Otte overall because it showed an escalating criminality that dated from his childhood. Otte responds that most of the information was presented by Dr. McPherson’s testimony anyway, and this explanation is therefore preposterous. We disagree.
The proposed testimony of Joslin and Bonham covered largely the same themes: that Otte was a sad and isolated, but affectionate, child. Joslin was adamant that Otte was not aggressive or a bully, but mentioned that he had stopped trying to buy the affection of his peers and was missing more school by the time she taught him in fifth grade. Bonham testified that Otte “was not a discipline problem to me. But because of his difficulties socially, I was concerned about that.” She also noted that his learning difficulties were not the worst in the class, which could have undermined the narrative of Otte’s difficult childhood. Otte’s actual school records would not have added much to all of this testimony, but could also have indicated a steady decline. McPherson’s testimony was similar in that it included Otte’s troubles at school and the fact that he was singled out and bullied by other children. Because her testimony was more limited in scope, however, it did not lend itself to the uncomfortable inference D’Angelo wanted to avoid; namely, that everyone around Otte perceived him as getting steadily more criminal and detached.
The post-conviction testimony of Katherine Hoffman, the drug-program administrator, was an extensive narrative on Otte’s drug use and his inability to fit into society. Among other things, she noted that Otte had been referred to an at-risk program because of “just a general sense that there were problems everywhere,” and seemed incapable of making any lasting progress: “[W]e would have some big intervention session, and I would feel like we had made some inroads.... And it seemed like we’d go away from there with great expectation, and then things never seemed to work for very long.” After Otte left the Gibault School, Hoffman’s testimony was that “I had this young man that I ... felt was just falling through the cracks, and it didn’t seem like we could get him to a place that he needed to be, and I was so worried about what was going to happen.” Dr. McPherson, on the other hand, presented all of the information that was helpful — that he was addicted to drugs, referred to social programs, did very well at the Gibault School, and was transferred out of it through no fault of his own — but with significantly less detail regarding Otte’s repeated failure to fit into society or the kind of lifelong downward spiral that might make Otte’s fate seem inevitable.
No one can know what evidence would have moved the panel to impose life on Otte instead of death. We might even agree with Otte that Hoffman and his teachers could have been helpful — they may have had more of a humanizing effect than the testimony of Dr. McPherson. But determining the optimal mitigation strategy is not our job. The question before us is narrow: was the state court’s decision to credit D’Angelo’s testimony and reasoning an unreasonable determination of the facts? The answer to that question is no. His inconsistencies were not sufficient to undermine his testimony that he agonized over what mitigation materials to present. His ra*605tionale for not presenting the materials is consistent with some of the damaging elements that Hoffman, Joslin, and Bonham might have introduced. The Ohio appeals court’s application of Strickland was therefore not unreasonable.
C. Miranda waiver
Finally, Otte contends that he lacked the ability to give a valid waiver of his privilege against self-incrimination under Miranda because he was suffering from the effects of drug and alcohol withdrawal. He was hospitalized for psychiatric evaluation on the evening of February 13, 1992, and hospitalized again for substance withdrawal in the early morning hours of February 15, 1992, only a few hours after he had given his first confession to the police. He further maintains that when he signed his written confession on February 16, 1992, he was not given Librium, a medication that had been prescribed to alleviate his alcohol-withdrawal symptoms.
The Fifth Amendment provides that “[n]o person ... shall be compelled in any criminal case to be a witness against himself.” In Miranda, 384 U.S. at 460-61, 86 S.Ct. 1602, the Supreme Court held that this right against self-incrimination “is fully applicable during a period of custodial interrogation.” In determining whether a waiver of this right is valid, we must determine whether it was made “voluntarily, knowingly, and intelligently.” Moran v. Burbine, 475 U.S. 412, 421, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986).
The inquiry has two distinct dimensions. 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 of both 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.
Ibid, (internal citations omitted). We must make these determinations on “the particular facts and circumstances surrounding th[e] case, including the background, experience, and conduct of the accused.” North Carolina v. Butler, 441 U.S. 369, 374-75, 99 S.Ct. 1755, 60 L.Ed.2d 286 (1979). We have held that “while our primary focus must remain on what the interrogating officers could have concluded about [a defendant’s ability to understand the warnings, we may consider later-developed evidence of a defendant’s actual mental ability to understand the warnings at the time of the interrogation.” Garner v. Mitchell, 557 F.3d 257, 263 (6th Cir.2009) (en banc).
Otte now argues that the Ohio courts’ application of Supreme Court precedent was unreasonable because the Ohio appeals court said that a showing of police coercion was necessary to invalidate a Miranda waiver, State v. Otte, No. 84455, 2005 WL 77071, at *6 (Ohio App.Ct. Jan. 13, 2005), because its factual conclusion that Otte was not impaired was also unreasonable, and because Otte’s confession was the product of police overreaching. We disagree.
The premise of Otte’s first argument is that a court must inquire into the defendant’s state of mind to determine whether a waiver is knowing and intelligent. We held en banc that the inquiry should be primarily on how the police officers perceived the defendant, Garner, 557 F.3d at 262-63. In any event, Otte’s argument fails because both the post-conviction trial *606court and the Ohio Court of Appeals performed the correct analysis by examining evidence of Otte’s subjective mental state during the relevant time period in determining whether the confession was valid. J.A. 14-17; Otte, 2005 WL 77071, at *6-7. Thus, they necessarily considered whether his confession was “knowing and intelligent,” as opposed to merely “voluntary.” Accordingly, we reject the notion that the state courts improperly required only a lack of coercion. In practice, the analysis of the state courts did not contradict the clearly established law of Moran.
As for the conclusions that Otte’s waiver was valid because Otte understood his rights and the police did not engage in any overreaching tactics, we cannot say that these determinations are unreasonable. At the post-conviction evidentiary hearing, Otte introduced the expert testimony of Dr. Smith that Otte was suffering from drug and alcohol withdrawal at the time of his waivers, and therefore he was not able to make the waivers knowingly, intelligently, and voluntarily. Smith testified that in his experience, people suffering from withdrawal of this type are very susceptible to pressure. The state introduced the testimony of Dr. Resnick, who concluded that Otte’s waiver was voluntary, knowing, and intelligent because there was no evidence that Otte was experiencing what were only possible effects of withdrawal. Dr. Res-nick found it significant that the officers did not notice any problematic symptoms and that Otte’s signature showed no signs of shakiness. In this duel between experts, the state court chose to credit Dr. Resnick. Otte has offered little more than competing testimony to show that Dr. Res-nick’s opinions were unsound. As we noted earlier, the state court’s decision to credit one expert over another is entitled to great deference. Otte also appeared to admit in the suppression hearing that he understood the waiver at the time he signed it.1 Therefore, it was not unreasonable for the state court to conclude that Otte knowingly and intelligently waived his Miranda rights.
As to the issue of voluntariness, the Ohio appeals court (on post-conviction review) looked to the previous decision of the Ohio Supreme Court (on direct review), which also rejected this claim. Otte, 660 N.E.2d at 718-19. In doing so, both courts relied upon the suppression hearing testimony of the interrogating officers. Detective Bomba, who interviewed Otte on February 13, testified that Otte did not appear to be under the influence of any substances. Detective DeSimone questioned Otte on February 14, and testified that Otte seemed composed and showed no physical symptoms of drug effects. Otte’s own testimony was that after DeSimone read Otte his Miranda rights, Otte indicated that he understood them and waived them. Otte claimed that DeSimone told him he could avoid the death penalty by confessing, but DeSimone denied making any such promise. DeSimone also testified that Otte appeared unaffected when he gave his written waiver and confession on February 16. The Ohio appeals court also emphasized Otte’s own testimony that he confessed because he felt bad. (Attorney: “Why did you make these admissions to Detective DeSimone?” Otte: “Well, first of all I felt bad.”). J.A. 147-48; Otte, 660 N.E.2d at 719. True, Otte points to some implausible elements in the officers’ testimony. The most notable of these is Detective DeSimone’s testimony that he was only indirectly aware that Otte — undoubtedly a *607high-profile suspect — had been sent to the hospital to be checked out. Otte also introduced booking sheets at his post-conviction hearing, which show that he was questioned on more occasions than the officers claimed (although the state offered evidence that booking sheets can over-represent the number of actual interviews). These arguments are far too speculative. Mindful of our deferential review, we conclude that Otte’s evidence is insufficient to render the state court’s decision unreasonable.
Ill
For the foregoing reasons, we AFFIRM the district court’s denial of Otte’s petition for habeas corpus.
. On cross-examination, Otte was asked, “[a]nd you signed your name and put yes, that you understood your rights, is that correct?” He responded, "Yes.” The attorney then asked, "[a]nd was that true at the time?" Otte responded, "Yes.”