James Collins stayed up late the night of April 30 to May 1, 2001, getting high on crack cocaine in his Chicago apartment with his girlfriend, Flora Lanier. Some*576time after 6:00 a.m., Collins and Lanier began fighting, a fight that ended when Lanier went through the window of Collins’ apartment, causing fatal wounds to both her arms. Collins, who has an IQ in the 60s and organic brain damage from an aneurysm in 1994, spent the next day at a police station before waiving his Miranda rights and giving a self-incriminating statement. The statement was admitted over his objection at trial, contributing to his conviction for first-degree murder. The Illinois courts have affirmed on direct appeal and post-conviction review, and the federal district court has denied Collins’ petition for a writ of habeas corpus. We now consider Collins’ appeal using the deferential standard that applies under the Antiterrorism and Effective Death Penalty Act. Because the state courts reasonably applied the correct legal standards and reasonably determined that Collins intelligently waived his Miranda rights, we affirm the denial of his petition.
I. Background
A. Procedural History
Following his statement to police, James Collins was indicted in the Circuit Court of Cook County, Illinois for first-degree murder. He filed two pre-trial motions, a motion to quash his arrest and a motion to suppress his statement. The trial court denied both of these motions.
Following a bench trial in late 2003, the state trial court convicted Collins of first-degree murder. The court found Collins not guilty of “intentional murder” but guilty of knowing acts that “created a strong probability of death or great bodily harm,” which also constitutes first-degree murder under Illinois law. See 720 111. Comp. Stat. 5/9 — 1(a). The trial court sentenced Collins to 25 years in prison. He appealed his conviction to the Illinois Appellate Court, claiming, among other things, that the trial court had erred in denying his motion to suppress. The Appellate Court affirmed the conviction on June 19, 2006, and the Illinois Supreme Court denied leave to appeal on November 29, 2006.
On March 22, 2007, Collins petitioned for state post-conviction relief based on other, unrelated issues. The trial court dismissed that petition as frivolous and Collins took no appeal.
Finally, on April 15, 2008, Collins filed his federal habeas petition, which the district court denied on March 26, 2009. The district court granted a certificate of appealability limited to the claim that Collins did not knowingly waive his Miranda rights.
B. The Night of April 30 to May 1, 2001
On the night Flora Lanier died, James Collins was 44 years old. Collins has long suffered from severe mental impairments. A brain aneurysm that he suffered in 1994 exacerbated those impairments, leaving him often unable to speak, understand, or think clearly. Defense experts calculated his current IQ in the low to mid-60s, well below the average score. A neurologist testifying for the defense estimated that Collins’ aneurysm had reduced his score by 10 to 15 points.
Collins began the night of April 30th in the company of his friend, Benny Price, who was homeless but had accepted Collins’ invitation to spend the night in his apartment. Between about 11:30 p.m. and 2:30 a.m., the two men ate dinner and talked in the apartment. Lanier showed up between 2:30 and 3:00 a.m. Price testified that he thought Lanier had been using PCP; she smelled of ammonia and seemed only periodically aware of her surroundings. Price had reason to know what a drug user looks like: the government im*577peached his testimony with a prior conviction for delivery of a controlled substance (and two for burglary).
Lanier had also brought rocks of crack cocaine for herself and Collins to smoke. Collins made clear to Price that the drugs were not for him, so Price went to sleep on the floor. Collins and Lanier shared a bed in the same room where Price was sleeping, with a makeshift barrier to give them some privacy. After going to bed, Price overheard Collins telling Lanier to stop taking people’s money to buy drugs for them and then keeping the money for herself. At that point Collins was calm, speaking in a “normal” tone and calling Lanier “baby.”
What happened next was the subject of dispute at trial. Price testified that he awoke around 6:00 a.m. to the sound of Collins and Lanier arguing and physically fighting. According to Price’s testimony, the combat was mutual, with both Collins and Lanier “wrestling.” Price testified that both Collins and Lanier were yelling; he heard Lanier yell, “Pm going to die anyway.” Not wanting to be around for this fight, Price immediately left the apartment. On the ground floor, he heard glass break and saw Lanier go through the third-floor window, then come back inside “real suddenly.” Lanier then “got on the kitchen table in front of the big window, and she hit it with her fist and leg,” then “stepped outside the window.” She remained “halfway out” for a moment before Collins “snatched her back inside.” As Collins pulled Lanier back in, “all the blood went down the window like that.”
From her apartment window one floor up, Ethel Patterson saw a different scene. Patterson testified at trial that Collins and Lanier were “tussling,” but Collins was the aggressor, “hitting her in the head with his fist,” while Lanier was in a purely defensive posture, with “her hands up over her head ... trying to block it.”1 Eventually Patterson saw Lanier “coming through the window ... with both hands forward.” Patterson denied at trial that Lanier “ran through the window” herself (though a police detective testified that this was contrary to what he had taken down from Patterson at the scene). After calling the police, Patterson saw Lanier bleeding profusely in the window and saying, “I am dying,” before Collins “jerked her back in.” Patterson went down to the third floor and found Lanier bleeding to death in the hallway; according to her testimony, all the doors were closed and no one was helping Lanier.
C. Police Investigation and Collins’ Statement
Chicago Police Officer Christopher Dobek and his partner were among the first law enforcement officers to arrive on the scene. Dobek testified that they received a dispatch call at about 6:45 a.m. and responded to Collins’ apartment. They found Lanier covered in blood but still alive in the hallway outside, and they called for an ambulance. Their knocking on Collins’ apartment door pushed the door partly open. The apartment was “in total disarray,” with “broken glass, blood all over the place.” Collins was inside, approaching the doorway, wearing only a pair of black pants, with blood on his hand and torso.
Paramedics took Lanier to the hospital, where she was pronounced dead. The medical examiner found evidence of injury to Lanier’s face, neck, chest, back, and extremities. Her most serious injuries were two “gaping” wounds, each three *578inches long, at the creases of Lanier’s right and left elbows, and another two-inch-long wound on her left inner forearm. The medical examiner’s opinion was that Lanier had died “as a result of multiple sharp force trauma due to an assault” and the “manner of death was homicide.” Blood testing revealed the presence of a cocaine degradation product, benzoylecgonine, in Lanier’s system.
Detective John O’Shea and his partner, Detective Joseph Laskero, arrived on the scene shortly after Lanier was taken away. O’Shea interviewed several witnesses, including Patterson and Price. Around the same time, two other uniformed officers spoke with Collins and asked him to come to the station with them for questioning. Collins agreed, and the officers brought him to a police station a few blocks away, arriving between 7:30 and 8:00 a.m. Collins waited there until 10:30 a.m., when O’Shea returned to the station. At that point, O’Shea read Collins a standard set of Miranda warnings and Collins agreed that he understood and wanted to speak. During this brief initial interview, Collins told O’Shea that Lanier had tried to jump through the window. O’Shea testified that, because this was inconsistent with what some of the witnesses had told him, he asked Collins to submit to a polygraph examination. Collins agreed, but an examiner was not available until 8:00 p.m. O’Shea left Collins in an interview room without Collins asking or O’Shea offering permission to leave.
The police left Collins alone during the nine hours that they waited for the examiner. He was allowed to leave the room to go to the bathroom. He was given food. He may have slept; O’Shea testified that he occasionally checked on Collins and saw him either on the floor or with his head down and arms folded on the table as if sleeping.
Eventually the polygraph examiner, Officer Robert Bartik, became free as scheduled, and officers took Collins from the local station to another police facility for the exam. From 8:00 to approximately 10:00 p.m., Bartik administered the polygraph. He first gave Collins fresh Miranda warnings and obtained Collins’ consent to submit to the exam. He then hooked Collins up and asked him nine questions, including whether Collins had pushed Lanier through the window and whether Collins had purposefully caused her injuries. Collins answered “no” to those questions, but the polygraph indicated that he was lying, and Bartik told him so.
Collins was then taken back to the local station, where he waited another hour or so until O’Shea returned. After once again advising Collins of his Miranda rights, O’Shea confronted him with the results of the polygraph. At 11:59 p.m., Collins gave an oral statement implicating himself in Lanier’s injury.2
The detectives left Collins in the interview room and called Assistant State’s Attorney Art Heil, who was on call for the State’s Attorney’s office that night. Heil arrived at the police station around 2:00 a.m. on May 2nd and learned the basics of the case from O’Shea and Laskero. The three of them then went back to Collins’ apartment building to view the scene and to speak again with Ethel Patterson, who was apparently willing to give the investigators an audience even in the middle of *579the night. They returned to the station around 6:00 a.m.
Heil then introduced himself to Collins for the first time, as “a lawyer and prosecutor, and not your lawyer.” He again explained to Collins his Miranda rights. Heil asked Collins to read a written statement of his Miranda rights aloud, then sign underneath to signify that he understood. Having done so, Collins talked with Heil for 45 minutes to an hour, after which Heil asked the detectives to leave the room. Outside their presence, Heil asked Collins if the police had treated him well and allowed him to eat and use the bathroom. Collins said that they had. Heil then proposed to memorialize in writing what Collins had told him. Collins agreed.
Heil began the written statement by asking Collins basic questions about himself and how he had been treated by the police, and writing down Collins’ answers. He proceeded to ask about the events leading to Lanier’s death. As Heil described it, “I would ask him a question. He would give me the response. I would write it down as he gave it to me. If I had questions, I would ask him questions back. I would prompt him with questions, asking him what happened next, so forth.”
When they were finished, Heil showed Collins the handwritten statement and had Collins read the first paragraph aloud. Then Heil read the rest of the statement aloud with Collins next to him. Collins, Heil, and one of the detectives signed the bottom of each page as they went along.
This is the substance of the statement that Heil took down at 7:00 a.m. on May 2nd and that the state court admitted over Collins’ objection, with emphases added:
James Collins states that he is 43 years old and that his birthday is June 27, 1956.3 James lives at 2910 West Harrison, number 301.
He has lived there for the past two years. James lives there with his girlfriend, Flora Lanier, who has lived with him for the past year and about eight months. James states that he can read and write English. James went to Crane High School where he attended through his senior year but he did not graduate.
James states that on the early morning of May 1, 2001, he and Flora had been up all night partying together. James states that they both smoked some crack cocaine. James states that around six o’clock a.m., he and Flora got into an argument. James states that the argument began over Flora not wanting to go to bed. James states that both he and Flora were yelling at each other and that Flora was disrespecting him and called him a bitch.
James states that the argument then became physical and he was hitting Flora. James states that he began hitting Flora because she made him so angry that he went berserk. James states that while they were fighting, he pushed Flora into the window and the window broke. James states that he pushed Flora because he wanted to hurt her and he was angry. James states that after Flora went into the window the first time, he continued to fight with her. James states that he continued to hit Flora because of his anger. James states that he then pushed Flora back into the window a second time and she broke the center window which is the bigger one. James states that he pushed her the second time because he was still trying to hurt her. James states that Flora went into the window and the glass broke. James states that *580he then saw Flora was cut and was bleeding. James states that Flora was bleeding a lot and holding her arms. James states that he still continued to struggle with Flora and she got blood on his pajama bottoms. James states that Flora broke free from him and ran out of the apartment.
James states that he did not go out after Flora and closed the door of the apartment behind her. James states that he did this because he just didn’t care about what happened to Flora.
James states that he then washed the blood off his hands and put on some pants over his bloody pajamas. James states that he then heard people outside in the hallway saying that they were going to call the police and an ambulance. James states that he then opened the door and saw Flora lying in the hallway bleeding. James states that he saw other people in the hallway but does not remember who was out there or how many. James states that he then said that Flora tried to jump out of the window herself but that was not the truth. James states that he said that because he knew what he did was wrong and he didn’t want to get in any trouble. James states that he stayed inside his apartment until the police arrived a short time later.
D. Evaluations of Collins and Evidence Presented at the Suppression Hearing
The state trial court heard testimony from four experts on Collins’ motion to suppress. Dr. Linda Wetzel, a clinical neuropsychologist who holds a Ph.D. from the Chicago Medical School, evaluated Collins on March 16, 2002, at the request of the defense. Dr. Susan Messina, a clinical psychologist who holds a Psy.D. from the Forest Institute of Professional Psychology, evaluated Collins in June, July, and September of 2002, on assignment from the state court. Dr. Linda Gruenberg, a psychiatrist whose qualification as an expert was stipulated by the parties, evaluated Collins on January 6 and February 10, 2003, at the request of the prosecution. Finally, Dr. Daniel Hier, a neurologist on the faculty of the University of Illinois, did not evaluate Collins personally but reviewed his medical records and expert evaluations and testified for the defense to interpret that medical evidence.
Dr. Wetzel, the defense neuropsychologist, testified that she ran a “standard battery of tests” on Collins and found that he performed poorly across a wide range of tests of mental ability. Collins scored 63 (two standard deviations below average) on the Wechsler Adult Intelligence Scale, a common IQ test, and tested at' a third-grade reading level. When Dr. Wetzel gave him the Trail A and Trail B tests, which are designed to assess functioning of the part of the brain regulating behavior, he tested “severely impaired” on Trail A and did so poorly on Trail B that Dr. Wetzel had to end the test without obtaining a result. She also tested for malingering and found no evidence that Collins was faking his impairments.
Dr. Wetzel also tested Collins specifically on his understanding of the Miranda warnings. She asked, one by one, if he knew what it meant that he had the right to remain silent, that anything he said could be used against him in court, that he had the right to a lawyer, and that a lawyer would be provided if he could not afford one. Asked about the first warning’s meaning, he said, “I don’t even have to say hello to you.” On the second, likewise: “I don’t even have to say hello to you.” On the third and fourth, Collins said, “You have the right to talk to a lawyer and have a lawyer present during questioning,” then, “I’m from the old *581school, I have morals, they incriminated on me.”
Dr. Wetzel concluded that Collins was unable to understand or waive his Miranda rights. This conclusion, she testified, was based on his low IQ, the severity of his past brain injury, his low reading and spelling scores, and impairment in his “self-regulation and his ability to really behave in an independent manner and to resist other people’s urgings and requests that he do things.” Although Dr. Wetzel conceded that Collins understood the words of the warnings, she “didn’t feel that he understood Miranda in the entire concept of Miranda ... the purpose of Miranda ... [or] the consequences of waiving Miranda.”
Both the government and the court questioned whether Dr. Wetzel, as a non-medical doctor, was capable of making an assessment of the effect of Collins’ brain injury on his mental ability. She conceded that she was not an M.D., but said that she based her assessment on “the severity that is mentioned on CAT scans and in the reports.” The aneurysm that Collins suffered, she testified, was “an elephant standing in the room” with regard to what caused his mental defects.
Dr. Messina, the clinical psychologist assigned by the court, testified that she had reviewed Collins’ police reports, statements, rap sheet, and psycho-social history before meeting with him. Like Dr. Wetzel, she ran a number of tests on Collins. He scored 65 on the Wechsler IQ test. On the Cognistat, which screens for neurocognitive limitations, Collins showed weakness in memory calculations, verbal-abstract reasoning, and information processing. Like Dr. Wetzel, Dr. Messina found no evidence of malingering. Dr. Messina testified that Collins “oftentimes became very tangential and disorganized” and used a number of “neologisms,” meaning that Collins often used a strange or incorrect word or combination of words.4
Dr. Messina went on to test Collins’ understanding of the Miranda warnings. On the first warning, he said, “It means something could be used against me. You don’t say nothing until your attorney is present.” On the second: ‘Whatever I said, it’s best to be the right vocabulary coming out of the volume. Then in court they can say, “You said this, that, woo, woo, woo.’ It’s always best to have your lawyer.” On the third, he said simply, “My lawyer.” And on the fourth: “They gonna give me one,” and “They didn’t give me one. He Shanghaied me. He didn’t give me no Miranda, just took me to the lockup.” Dr. Messina conceded that Collins “understands the meaning” of the words in the warnings. She concluded, however, based on her interviews and testing, that Collins would not have been capable of understanding or appreciating his Miranda rights when he spoke with police.
Dr. Gruenberg, the psychiatrist for the state, testified that she had reviewed Dr. Wetzel’s and Dr. Messina’s reports, as well as the other police and medical reports in Collins’ record, before evaluating him. Dr. Gruenberg evaluated Collins’ mental ability by asking him a series of questions and interpreting the answers that Collins gave. Dr. Gruenberg testified that she “review[ed] very carefully” the other experts’ evaluations and the tests they gave, but “would not be in a position to evaluate the *582manner in which the tests were given or which they were read.” Although she had no dispute with the results of the tests the other experts had given, Dr. Gruenberg testified that comprehension of the warnings “is a very specific question that I was able to determine he is able to do based upon my interview, regardless of the results of the tests [Dr. Messina and Dr. Wetzel] performed.”
In her interview with Collins, Dr. Gruenberg asked what first degree murder was; Collins responded that that was what he was charged with. Pressed further, he said that it meant premeditated. Asked what “premeditated” meant, he answered “killing someone and knowing what you are doing.” Dr. Gruenberg asked what the police are supposed to say before questioning him, and Collins responded that “the police are supposed to say you have a right to remain silent and what you say can be used against,” which she read as having some understanding of the warnings. Asked again later what the Miranda warnings were, Collins responded: “you have the right to remain silent, anything you say may be used against me.” Dr. Gruenberg also testified that Collins acknowledged that he could stop speaking to her at any time, and that what he told her would be presented in court.
Dr. Gruenberg also asked Collins about the meaning of each specific warning. To the first warning, Collins said, “zip it, shut up, don’t talk, like a mannequin. Don’t talk no matter how bad. Don’t have to say.” To the second: “Even like I explained to you about everything that I say can be used against you, like you told me from the state when you first came here.” Dr. Gruenberg interpreted this response to mean that Collins was “recalling again that he knew I was from the state,” and that “he had an understanding that state was opposing him.” To the third warning, Collins said, “the consequences of that could be devastating, overwhelming, but that he did not need an attorney to answer the questions,” and “no, I didn’t need an attorney because I didn’t do anything that I needed an attorney to defend on.” To the fourth, Collins said, “it is clear,” and “you said it.”
Another line of questions concerned the consequences of speaking. Asked the meaning of “consequence,” Collins answered, “regret or semi fortunate or unfortunate,” and “do nothing or do something,” and “don’t do it, but if I do, will suffer the consequence and that is on the unfortunate part that this is happening and might regret it. And might not.” Elaborating, Collins said, “there are consequences that depend on present time. And the consequence is whatever happened after I did it.” Asked specifically about the consequences of giving a statement, Collins said, “just like I did, look what happened to me.” Dr. Gruenberg believed that this referred to the fact that he had been arrested and incarcerated.
Unlike Dr. Messina and Dr. Wetzel, Dr. Gruenberg did not believe Collins was overly compliant to the will or instruction of others. In support, she testified that she had asked Collins if he would be concerned about her feelings if he wanted to terminate the interview. Collins responded that he was “not concerned about my feelings and said that he would be able to say to me nicely that I don’t want to talk on and then leave.”
Dr. Gruenberg concluded from all of her questioning that, at the time she interviewed him in January and February 2003, Collins was able to understand his Miranda rights and the consequences of waiving those rights. She would not offer an opinion on his ability to understand the rights or consequences of waiver when he gave his statement to police, unless his *583mental state was “similar to the state which he had at the time I evaluated him,” a subject on which she offered no opinion.
The last doctor in line was Dr. Daniel Hier, the neurologist who testified for the defense. Dr. Hier did not evaluate Collins personally, but rather testified from a medical doctor’s perspective about the likely effects of the brain aneurysm that Collins suffered in 1994. He reviewed Collins’ medical records from 1994 up to May 2001, as well as the reports and testimony of all the experts who had come before him. Dr. Hier clarified the medical record, corrected a few factual mistakes, and answered questions that the earlier experts had felt unqualified to answer.
Dr. Hier began by explaining that Collins’ brain had suffered a mycotic aneurysm, which occurs when an artery is weakened by bacterial infection. This aneurysm was not, as the court had surmised and Dr. Wetzel had believed, the kind of aneurysm that can be treated by “clipping” and isolating it from circulation. Dr. Hier went on to explain the procedures that Collins underwent to treat the aneurysm and the physical damage that the aneurysm caused. Specifically, he testified to two kinds of damage: structural damage, namely, a hole in Collins’ brain that was filled with spinal fluid, along with large areas of hemorrhage in both frontal lobes of the brain; and neuropsychological damage flowing from that structural damage.
Asked how one would measure this neuropsychological damage, Dr. Hier answered that he would begin by testing for sensory loss or loss of coordination. Finding no evidence of that here, he would proceed to do “detailed neuropsychological evaluation to determine if there are any neuropsychological problems compatible with this hemorrhage.” According to Dr. Hier, the results of the tests that Dr. Wetzel and Dr. Messina performed provided evidence of “deficits in neuropsychological functioning in Mr. Collins which were compatible with” the kind of injury that Collins had suffered. Dr. Hier explained further that the frontal lobes “play the lead role in what’s called executive functioning,” which he defined as “the ability of the person to have insight into1 their own behavior, to plan for the future, to stay organized, to stay focused on task,” among other things. The frontal lobes, which bore the brunt of the aneurysm’s damage, are also important in “memory and language.”
Dr. Hier testified that he believed Collins’ brain injury had caused him to suffer from expressive aphasia, a language disorder consistent with Collins’ odd manner of speech. A more difficult question, Dr. Hier acknowledged, was whether Collins also suffered from receptive aphasia, or a defect in his ability to understand words spoken by others. Dr. Hier conceded that none of the experts had performed a test specifically designed to diagnose that condition. But Collins’ poor performance on a subtest of the Wechsler IQ test suggested to Dr. Hier that Collins had at least mild receptive aphasia. This testing, he said, was “quite good and I believe quite valid.”
Dr. Hier offered no opinion on whether Collins was able to understand the Miranda warnings. He did offer, in response to questioning by the trial judge, a few words of disagreement with Dr. Gruenberg’s interpretation of Collins’ responses to her questions: “I found his responses kind of vapid, empty, vacuous and not reflecting a lot of understanding as to what the Miranda rights really entailed. She took a different interpretation to it ... but again these are two different people interpreting the same information.”
The state trial court also considered evidence from the written report of a fifth *584doctor, Philip Pan. Dr. Pan, a psychiatrist, was assigned by the court to evaluate Collins on October 10, 2002. Dr. Pan concluded that “the available evidence indicates that the defendant has an adequate understanding of his rights under Miranda.” He added, however: “I apologize to the Court that I am unable to reach an opinion to the requisite degree of certainty whether defendant was able to understand and competently waive his rights under Miranda at the time of his arrest and questioning. His documented cognitive deficiencies, the possible effects of drug intoxication or withdrawal with crack cocaine, and an overwhelmed and distraught emotional state leads to a murky reconstruction of the defendant’s likely mental state at that time.”
The court also heard from Prosecutor Heil, Detective O’Shea, and Officer Bartik, all of whom testified that they gave Collins Miranda warnings before each interview and obtained his agreement that he understood. They also testified that Collins never seemed confused about what they were telling or asking him. In addition, the court heard evidence that Collins had been arrested four previous times, three times in 1998 and once in 1997, and each time had been given Miranda warnings.
The trial court denied the motion to suppress in a written opinion. The court gave a full summary of the evidence presented at the suppression hearing, including the testimony of the four experts, Prosecutor Heil, and the police witnesses. After laying out the legal standard for intelligent waiver of Miranda rights, the court held that, although the evidence supported the defense argument that Collins suffered intellectual deficits, it also showed that Collins was able to understand his rights and the warnings he was given to the necessary degree. In reaching this conclusion, the court considered Collins’ responses to the experts’ questions, the number of times he was given warnings on this occasion and in the past, and his initial denial of responsibility for Lanier’s injuries.
On appeal, the Illinois Appellate Court recapitulated the evidence and held that the trial court had not erred in admitting the statement. The Appellate Court followed the trial court’s reasoning, holding that the “conflicting evidence in the record, as well as effective impeachment of the defense experts,” was sufficient to affirm the trial court’s decision as reasonably supported by the evidence.
II. Analysis
The Antiterrorism and Effective Death Penalty Act (AEDPA) governs federal judicial review of a petition for writ of habeas corpus from a person in custody pursuant to a state court judgment. See 28 U.S.C. § 2254. Under the AEDPA, a federal court may not issue a writ of habeas corpus unless the state court’s adjudication of the petitioner’s claim either “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 “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). Collins contends that the Illinois state courts’ adjudication of his claims did both.
A. Contrary to or Unreasonable Application of Federal Law
Collins’ first argument is that his petition should be granted because the Illinois courts’ decisions were contrary to or unreasonable applications of clearly established federal law as determined by the United States Supreme Court. See 28 *585U.S.C. § 2254(d)(1). The Supreme Court has explained that a decision is “contrary to” federal law when it “contradicts the governing law set forth in our cases,” or when “the state court confronts a set of facts that are materially indistinguishable from a decision of this Court and nevertheless arrives at a result different from our precedent.” Williams v. Taylor, 529 U.S. 362, 405-06, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court decision involves an “unreasonable application of’ federal law when it “correctly identifies the governing legal rule but applies it unreasonably to the facts of a particular prisoner’s case,” id. at 407-08, 120 S.Ct. 1495, but not when the state court merely applies federal law “erroneously or incorrectly,” id. at 411, 120 S.Ct. 1495. In other words, the state court’s application of federal law must be “well outside the boundaries of permissible differences of opinion.” Jackson v. Frank, 348 F.3d 658, 662 (7th Cir. 2003), quoting Hardaway v. Young, 302 F.3d 757, 762 (7th Cir.2002) (quotation marks omitted). Here the state courts’ decision was neither contrary to nor an unreasonable application of clearly established federal law as determined by the Supreme Court.
Collins contends that the Illinois courts failed to hold the government to the “heavy burden” of proving that he validly waived his rights under Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). It is true that the Supreme Court used those words and the Illinois courts did not. But more than that is required to satisfy the standard of § 2254(d)(1). The state courts recited and applied the well-established requirement that a defendant’s waiver must be both voluntary, meaning non-coerced, and intelligent, meaning with “a full awareness of both the nature of the right being abandoned and the consequences of the decision to abandon it.” See Moran v. Burbine, 475 U.S. 412, 421, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986); accord, Colorado v. Spring, 479 U.S. 564, 573-74, 107 S.Ct. 851, 93 L.Ed.2d 954 (1987); Edwards v. Arizona, 451 U.S. 477, 482-83, 101 S.Ct. 1880, 68 L.Ed.2d 378 (1981); Tague v. Louisiana, 444 U.S. 469, 471, 100 S.Ct. 652, 62 L.Ed.2d 622 (1980) (courts may not presume that waiver was voluntary and knowing; state must meet “heavy burden” of showing voluntary and knowing waiver).
The state courts also applied the proper standard for intelligent waiver. The trial court wrote that the “awareness component does not require knowing and understanding every possible consequence of a waiver ... but rather simply being cognizant of the State’s intention to use one’s statement to secure a conviction and of the fact that one can stand mute and request a lawyer.” The trial court properly cited Burbine and Oregon v. Elstad, 470 U.S. 298, 105 S.Ct. 1285, 84 L.Ed.2d 222 (1985), the Supreme Court’s central cases on this question. For its part, the Appellate Court cited only Illinois cases but used the same correct standard.
Collins also argues that the state court’s decision was contrary to federal law because it failed to require the government to show that police took “special care” in obtaining a voluntary waiver given his limited mental capacity. We disagree. The Supreme Court has said that when the police are aware of a suspect’s mental defect but persist in questioning him, such dogged persistence can contribute to a finding that the waiver was involuntary. See Mincey v. Arizona, 437 U.S. 385, 398-99, 98 S.Ct. 2408, 57 L.Ed.2d 290 (1978) (suspect’s waiver was involuntary when police officer questioned him while he was “confused and unable to think clearly,” in critical condition in a hospital bed). The Court has also held that a suspect’s mental capacity is a factor that a court must con*586sider in deciding whether a waiver was voluntary. See Fare v. Michael C., 442 U.S. 707, 724-25, 99 S.Ct. 2560, 61 L.Ed.2d 197 (1979), citing North Carolina v. Butler, 441 U.S. 369, 373, 99 S.Ct. 1755, 60 L.Ed.2d 286 (1979). The Court has never held, however, that police can render a waiver of Miranda rights involuntary simply by failing to take “special care” that a suspect with a mental disability understands his rights.
Even if the Supreme Court had clearly established a “special care” requirement in its precedents, the state courts’ failure to apply such a requirement here would not have met the standard imposed by § 2254(d)(1) for habeas relief. Collins produced no evidence that the police officers who examined him were aware of his mental deficiency. Indeed, his trial counsel barely cross-examined Prosecutor Heil and Detective O’Shea on this point, and his appellate counsel conceded at oral argument that she was not claiming the police illegally coerced Collins into giving a statement.
B. Unreasonable Determination of the Facts
The state courts were right on the legal standard and applied that legal standard reasonably to the facts that they had determined. But Collins has also challenged whether the state courts were reasonable in finding those facts. The AED-PA permits a federal court to grant a petition for writ of habeas corpus if the state court’s decision is “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)(2).5
Under this standard, a state court’s factual finding is never unreasonable “merely because the federal habeas court would have reached a different conclusion in the first instance.” Wood v. Allen, — U.S. --, 130 S.Ct. 841, 849, — L.Ed.2d —— (2010). Rather, the state court’s determination of the facts must have been an unreasonable error in light of the evidence presented to that court. Ward v. Sternes, 334 F.3d 696, 703-04 (7th Cir.2003). Because the Illinois Supreme Court denied review, we look to the opinion of the Illinois Appellate Court, as well as to the written opinion of the trial court, whose reasoning and outcome were followed and affirmed on appeal.
For a defendant to have validly waived his rights under Miranda, two distinct facts must be true. First, the defendant must have waived his rights “voluntarily.” Miranda v. Arizona, 384 U.S. 436, 444, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). In other words, the waiver must have been “the product of a free and delib*587erate choice rather than intimidation, coercion, or deception.” Moran v. Burbine, 475 U.S. 412, 421, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986); accord, Colorado v. Spring, 479 U.S. 564, 573-74, 107 S.Ct. 851, 93 L.Ed.2d 954 (1987). Second, the defendant must have waived his rights “knowingly and intelligently.” Miranda, 384 U.S. at 444, 86 S.Ct. 1602. In other words, the “totality of the circumstances surrounding the interrogation” must show that the defendant had “a full awareness of both the nature of the right being abandoned and the consequences of the decision to abandon it.” Burbine, 475 U.S. at 421, 106 S.Ct. 1135; accord, Spring, 479 U.S. at 574, 107 S.Ct. 851.6
As we have noted, Collins does not seriously contend here that his waiver was involuntary. Nor could he, because there is no evidence that the police sought to obtain a confession despite his will to remain silent or to have a lawyer present during questioning. Collins went voluntarily to the police station. Although he remained in an interview room for nine hours waiting for a polygraph examiner to become available, he was given food and drink, was allowed to use the bathroom, and was otherwise left alone. He never invoked his right to remain silent or to see a lawyer. The police gave him Miranda warnings each time he was questioned and had him acknowledge his waiver. There is no evidence that they knew about his mental disability and sought to take advantage of it.
But even in the absence of intentional coercion, if Collins had insufficient mental capacity to understand what the officers and prosecutor were saying to him, he could not have waived his rights. What level of understanding, then, does Miranda require before a defendant can intelligently waive his rights and give an admissible statement?
The Supreme Court has offered some limited guidance on this question, usually by telling lower courts what the government need not show in order to prove a valid Miranda waiver. “The 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. *588at 574, 107 S.Ct. 851, citing Burbine, 475 U.S. at 422, 106 S.Ct. 1135; Elstad, 470 U.S. at 316-17, 105 S.Ct. 1285. A waiver is valid “if the defendant fully understands the nature of the right and how it would likely apply in general in the circumstances — even though the defendant may not know the specific detailed consequences of invoking it.” United States v. Ruiz, 536 U.S. 622, 629, 122 S.Ct. 2450, 153 L.Ed.2d 586 (2002). For example, a defendant may waive his right to remain silent even if he “does not know the specific questions the authorities intend to ask.” Id. at 629-30, 122 S.Ct. 2450.
The federal Courts of Appeals, including this circuit, have followed the Supreme Court’s instructions by requiring the government to clear only a relatively low bar in proving an intelligent waiver. Generally, the courts will hold that a defendant’s waiver is knowing if he understands that he can refuse to talk to the people asking him questions or stop the questioning once it begins; that the people asking him questions are not his friends but are police or law enforcement personnel who are trying to show he is guilty of a crime; that he can ask for and get a lawyer who will help him; and that he does not have to pay for that lawyer. See, e.g., Smith v. Mullin, 379 F.3d 919, 933-34 (10th Cir.2004) (mentally disabled defendant gave intelligent waiver where he understood “the role of police officers and the concept of a criminal charge,” “comprehended the questions the officers presented,” and had been arrested and served time in prison before); Henderson v. DeTella, 97 F.3d 942, 948-49 (7th Cir.1996) (waiver was intelligent where defendant had below-average IQ but understood the nature of the charges, initially declined to speak, and had been prosecuted as a juvenile); United States v. Frank, 956 F.2d 872, 877-78 (9th Cir.1991) (no clear error in admitting statement where a Navajo man who knew nothing about the American legal system understood that he could remain silent, that a defense lawyer is “someone who helps you,” and that a prosecutor “does not help you”). It is only when the evidence in the case shows that the defendant could not comprehend even the most basic concepts underlying the Miranda warnings that the courts have found an unintelligent waiver. One example is a defendant whose command of English is so poor that the police might as well have been speaking gibberish. See, e.g., United States v. Alarcon, 95 Fed.Appx. 954, 955-57 (10th Cir.2004) (defendant understood only “bits and pieces” of English and often pretended to understand English out of embarrassment and a desire to cooperate); United States v. Garibay, 143 F.3d 534, 537-38 (9th Cir.1998) (no evidence that defendant spoke enough English to understand warnings, and several witnesses testified that he spoke only a few words of English).
The state courts found that Collins understood enough of the police and prosecutor’s warnings to satisfy Miranda’s requirements. We cannot say that finding was unreasonable, although this is by no means an easy case. As the state courts acknowledged, Collins produced significant evidence of his limited mental capacity at the time he gave his statement. The state courts gave due consideration to that evidence. Our deferential evaluation of the record leads us to conclude that the state courts were not unreasonable in determining that Collins nevertheless understood to the requisite degree both the Miranda warnings and the consequences of waiving his rights.
To begin with, the testimony of the expert witnesses at the suppression hearing does not compel us to find that Collins was incapable of giving an intelligent waiver. Dr. Wetzel and Dr. Messina both testified to that ultimate legal conclusion, but an *589expert’s testimony about an ultimate issue is most valuable when it is amply supported by the rest of her testimony. See, e.g., Huey v. United Parcel Service, Inc., 165 F.3d 1084, 1087 (7th Cir.1999) (an ultimate conclusion without analysis is “meaningless”). These experts’ supporting testimony does not convince us that the state courts were unreasonable in rejecting their final opinions. Dr. Wetzel’s testimony that Collins “was able to paraphrase each sentence” of the warnings and understood “that he doesn’t have to talk,” but was “unable to really elaborate” on his rights and could not understand “the entire concept of Miranda ” or “the purpose of Miranda,” leads us to suspect that Dr. Wetzel applied a more rigorous standard of understanding than the Supreme Court requires. Likewise, Dr. Messina testified that Collins was able to tell her, in his own words, what each of the warnings meant. Though Collins’ manner of speaking sometimes clouded what he was trying to say, he was able to get across that “something could be used against me,” that “you don’t say nothing until your attorney is present,” that if you speak to police, then “in court they can say, ‘You said this, that, woo, woo, woo,’ ” and that if he could not afford a lawyer, “They gonna give me one.” This is not the kind of utter incomprehension that would compel a result contrary to the one the state courts reached.
The answers that Collins gave to the state’s psychiatrist, Dr. Gruenberg, reinforce this conclusion. Collins was able to understand and explain the meaning of premeditated murder. He understood what a consequence was and suggested that his current situation was a consequence of waiving his rights. And, as he had with Dr. Messina, Collins rephrased each of the Miranda warnings in a way that gives us confidence that the state courts were not unreasonable in finding his waiver was intelligent. He knew the right to remain silent meant to “zip it, shut up, don’t talk, like a mannequin ... don’t have to say”; if he did speak, “everything that I say can be used against you, like you told me from the state when you first came here”; he knew he could have a lawyer, but “I didn’t need an attorney because I didn’t do anything that I needed an attorney to defend on”; and the final warning was so “clear” that he could simply say, “You said it.” Of course, not everything that Collins said to Dr. Gruenberg was the picture of clarity and comprehension, and some of the inferences she drew from his answers were unpersuasive. On the whole, however, Dr. Gruenberg’s testimony went a long way toward supporting the reasonableness of the state courts’ factual determination.
Finally, the testimony of Dr. Hier, though useful in connecting Collins’ medical history of organic brain damage to the other experts’ testimony about his mental disability, did not render the state courts’ determination unreasonable. Dr. Hier is among the preeminent physicians in his field, and his testimony confirmed that the aneurysm that Collins suffered made an already weak mind even weaker. But Dr. Hier offered no definitive opinion on whether Collins was able to understand the warnings that the police gave before interrogating him, or on whether he was able to understand what a waiver entails. To the extent he disagreed with Dr. Gruenberg’s interpretation of the responses Collins gave in Dr. Gruenberg’s own interviews, the state courts were not unreasonable in siding with Dr. Gruenberg. In short, Dr. Hier’s testimony supports a finding that Collins was mentally impaired; it does not compel a finding that Collins was so impaired that he could not have understood his rights.
Our conclusion that the state courts’ determination was reasonable finds further *590support in evidence that Collins was able and willing to deceive or even lie to investigators. In his first interview with Detective O’Shea on the morning of May 1st, Collins told O’Shea that Lanier “ran through the window,” suggesting he had not pushed her. During the polygraph exam, Collins again indicated that he was not responsible for Lanier’s death. It was only when Detective O’Shea confronted Collins later with the results of the exam— results that indicated Collins was being deceitful — that Collins changed his story and implicated himself in causing Lanier’s injury. It was not unreasonable for the state courts to infer from Collins’ changing story that he knew how to deceive and understood the situation that he was in when the police took him to the station.
It was also reasonable for the state courts to discount the effect that Collins’ drug use and possible emotional or physical strain had on his ability to understand the Miranda warnings and the consequences of waiving them at the time of the interrogations. We do not know how much cocaine Collins ingested the night Lanier died. We do not know how much he slept that night, or during the day of May 1st while waiting for the polygraph examiner to become free, or on the night of May 1st to 2nd while the investigators were away. We do not know what emotional harm, if any, he suffered from the fight with Lanier and his subsequent detention at the police station. AJI of this uncertainty is likely what led Dr. Pan and Dr. Gruenberg to decline to offer an opinion on Collins’ mental capacity at the time of his statement.
What we do know is what was said by the law enforcement officials who saw and spoke with Collins at the time. Detective O’Shea testified that when he spoke to Collins at 10:30 a.m. on May 1st, Collins’ demeanor was “calm and cooperative.” Likewise, Officer Bartik, the polygraph examiner, testified that Collins appeared fine during the exam. Finally, Prosecutor Heil testified that Collins “seemed fine” when they spoke at 6:00 a.m. on May 2nd, just before Collins gave his statement. According to Heil’s testimony, Collins denied being under the influence of alcohol or drugs. And although the testimony of the investigators alone does not present a full picture, Collins himself never offered any testimony or evidence that he was so influenced by drugs or by emotional or physical trauma that he could not have understood the warnings or the consequences of waiver. In the absence of any such evidence, it was not unreasonable for the state courts to discount those possible influences on his mental capacity.
The Miranda warnings represent a balance between the desire to obtain truthful confessions and the desire to protect some of our most fundamental rights. To strike this balance effectively, we do not require that a criminal suspect understand every consequence of waiving his rights or make the decision that is in his best interest. The Illinois courts understood and reasonably applied the federal constitutional standard. Viewing the record through the AEDPA lens, we cannot say that the state courts’ determination that Collins met that standard was unreasonable. We therefore Affirm the district court’s denial of Collins’ petition for writ of habeas corpus.