
574 F.3d 1354 (2009)
Elmer Leon CARROLL, Petitioner-Appellant,
v.
SECRETARY, DOC, FL Attorney General, Respondents-Appellees.
No. 08-14317.
United States Court of Appeals, Eleventh Circuit.
July 17, 2009.
*1356 Michael Paul Reiter (Court-Appointed), Venice, FL, for Carroll.
Scott Andrew Browne, Tampa, FL, for Respondents-Appellees.
Before BLACK, HULL and WILSON, Circuit Judges.
BLACK, Circuit Judge:
Elmer Leon Carroll, a Florida prisoner under a sentence of death, appeals the district court's order denying his 28 U.S.C. § 2254 petition for a writ of habeas corpus. The district court granted a certificate of appealability as to the second claim from Carroll's petition: Whether Carroll was denied his rights of due process and equal protection when the state court failed to grant an evidentiary hearing on his claim of mental retardation and mental illness under Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). After review and oral argument, we affirm the district court's order.

I. FACTS

A. The Crime
The facts of the underlying crime are gathered largely from the Florida Supreme Court's decisions affirming Carroll's conviction and sentence, Carroll v. State, 636 So.2d 1316 (Fla.1994) (Carroll I), and the trial court's denial of Carroll's first 3.850 motion for post-conviction relief, Carroll v. State, 815 So.2d 601 (Fla.2002) (Carroll II).
On October 30, 1990, at about 6 a.m., Robert Rank went to awaken his ten-year-old stepdaughter, Christine McGowan, at their home in Apopka, Florida. When Christine did not respond to his calls, Rank went into her bedroom and found her dead. Shortly thereafter, Rank noticed his front door was slightly ajar and his pickup, in which he had left the keys, was missing. When the police arrived, they determined Christine had been raped and strangled. A BOLO was issued for the missing truck, which was a white construction truck bearing the logo ATC on the side.
Shortly thereafter, the truck was seen parked on the side of a highway, and Carroll was observed walking about one mile down the road from the truck. Carroll was subsequently stopped and searched, and the keys to the truck were found on Carroll. Two witnesses had also observed Carroll driving the truck earlier that morning. Blood was found on Carroll's sweatshirt and genitalia, and semen, saliva, and pubic hair recovered from the victim were later determined to be consistent with that of Carroll.
On November 26, 1990, Carroll was indicted on one count of first-degree felony murder and one count of sexual battery on a person less than twelve years of age.


*1357 B. The Competency Hearing

In August 1991, Carroll's trial counsel, James E. Taylor, Jr., became "increasingly concerned" that Carroll did not understand the gravity of the charges against him and was incapable of assisting in his defense. Taylor filed a motion for a competency hearing, in which he proffered the opinions of two licensed psychiatrists who believed Carroll was not competent to stand trial. Judge Jeffords D. Miller granted the motion and appointed five experts to evaluate Carroll to determine if he was competent to stand trial. Pursuant to the court's order and Florida Rule of Criminal Procedure 3.211, any expert who determined Carroll was not competent was also required to inform the court as to "[t]he nature and extent of the mental illness or mental retardation suffered by the Defendant" and "[w]hether the Defendant, because of such mental illness or mental retardation, meets the criteria for involuntary hospitalization or placement as set forth by law." In addition to evaluating Carroll for competency, the experts were also asked to examine Carroll as to his sanity at the time of the alleged offense.
On November 15, 1991, Judge Miller heard testimony from Dr. Edward Benson, Dr. Robert G. Kirkland, Dr. Michael E. Gutman, and Dr. Jeffrey A. Danziger, all of whom were psychiatrists, regarding Carroll's competency to stand trial.[1] Of the experts, only Dr. Benson testified he believed Carroll was not competent to stand trial. Dr. Benson had evaluated Carroll twice after his arrest, and at both times Dr. Benson believed Carroll was not competent. Dr. Benson first examined Carroll on December 11, 1990, at which time he observed Carroll "was actively psychotic, schizophrenic, and ... he was very delusional, and . . . very incoherent, very withdrawn." Dr. Benson again examined Carroll on October 11, 1991, and determined Carroll was still "quite psychotic" although "he had been previously much more psychotic last year." Following the October 1991 evaluation, Dr. Benson submitted a written report to the court in which he diagnosed Carroll with schizophrenia and a paranoid-type personality disorder; the report also noted Carroll had a borderline intelligence quotient (IQ), based upon the results of previous psychological testing.
Like Dr. Benson, Dr. Kirkland testified he had evaluated Carroll multiple times. Dr. Kirkland first evaluated Carroll shortly after his arrest and concluded "[t]here was an indication of possible emotional or mental disorder." Following this evaluation, Dr. Kirkland recommended Carroll was not competent to stand trial and committed him to the intensive psychiatric unit at Florida Hospital under Dr. Kirkland's care. There, Carroll underwent psychological testing and "although there were some indicators of possible psychosis, the main thread seemed he was malingering." After spending several days at Florida Hospital, Carroll returned to the Orange County Jail where Dr. Kirkland continued to monitor him. On October 10, 1991, Dr. Kirkland again evaluated Carroll, at which time he concluded that Carroll was legally sane and competent to stand trial and that he suffered from antisocial personality disorder. Citing lack of investigative reports of the crime, however, Dr. Kirkland declined to give an opinion as to Carroll's mental condition at the time of the offense.
*1358 In addition to Dr. Kirkland, Dr. Gutman also testified he believed Carroll was competent to stand trial. Dr. Gutman testified he examined Carroll once, on September 26, 1991, and reviewed medical information dating back to 1980, jail clinic files, and investigative reports dealing with the alleged offenses. Based upon his own evaluation and the reports provided to him, Dr. Gutman made a diagnosis "that [Carroll] has a substance abuse problem with alcohol and drugs; that he was malingering at the time I saw him; and that he has a long term character and behavior disorder with antisocial passive/aggressive and borderline personality traits." In his written report to the court, Dr. Gutman added he believed Carroll was "of average to high average intelligence," despite a score of 60 on an IQ test performed at Florida Hospital shortly after the arrest, and noted "[t]his inconsistency would point to conscious efforts to look retarded or mentally ill." Dr. Gutman declined to offer an opinion on Carroll's mental status at the time of the offense, citing lack of information provided by Carroll.[2]
Dr. Danziger was the last expert witness to testify at the competency hearing. Dr. Danziger evaluated Carroll on October 14, 1991; he also reviewed Carroll's medical records, jail clinic files, and investigative reports to help formulate his opinions. On the basis of his evaluation and the other information supplied to him, Dr. Danziger, like Dr. Kirkland and Dr. Gutman, testified he believed Carroll was competent to stand trial. Dr. Danziger also provided a written report to the court, in which he diagnosed Carroll with "Schizophrenia, Chronic Undifferentiated Type," alcoholism, and multiple drug abuse; he added he believed Carroll was "genuinely psychotic" the night of the offense, but admitted that he offered the opinion "without much certainty or forcefulness" and that "[t]his is probably one of those opinions that is a 51% for and 49% against." His report also noted Carroll's psychological testing results from Florida Hospital; these results included a verbal IQ score of 58, which the doctor who conducted the testing determined "was not reliable and underestimated [Carroll's] intelligence because he was not cooperating." Based upon his own observations, Dr. Danziger described Carroll's intellect as "roughly in the average to below average range" and concluded "[t]here was no evidence to suggest that he had mental retardation."
After considering the testimony from the competency hearing and the reports of the four experts who testified, Judge Miller found Carroll was competent to proceed to trial and to assist his attorney in preparation of his defense and issued an order to that effect on December 27, 1991.

C. The Jury Trial
The case proceeded to trial on March 16, 1992, with Judge Belvin J. Perry, Jr., presiding. In addition to contesting guilt, Carroll also raised a defense of insanity. The State and the defense presented conflicting testimony from five expert witnesses, including the four experts who had testified at the competency hearing, on Carroll's mental status at the time of the offense.
During the State's case in chief, Dr. Gutman again testified regarding his diagnosis of Carroll. He told the jury that Carroll had "a long term character and behavior disorder," which included antisocial personality traits, passive/aggressive personality traits, borderline personality traits, and paranoia. He added, however, *1359 that he believed Carroll was malingering during his examination and "acting in a fraudulent way to present himself in a sicker fashion than was actually the case." Based upon his examination of Carroll, Dr. Gutman determined Carroll was "in the high average range of intelligence," which would have placed his IQ "somewhere around 105 to 110." Dr. Gutman attributed lower IQ test scores, some of which were in the 60-to-69 range, to malingering. He explained Carroll was "capable of distorting, consciously distorting the answers so that the evaluator would come up with certain answers, would come up with certain responses that could indicate that he had a low IQ, when in truth the answers that he gave me and the savvy and awareness that he had would indicate a higher IQ." Consistent with the report he submitted to the court in conjunction with the competency hearing, Dr. Gutman testified he was unable to make a determination as to whether Carroll was legally sane at the time of the offense because Carroll claimed he could not recall any information regarding the crime.
Dr. Benson, Dr. Danziger, and Dr. Elizabeth McMahon, a clinical psychologist, testified for the defense. Dr. McMahon, the only expert who did not also testify at the competency hearing, examined Carroll for three hours on November 1, 1990, just two days after the murder. During that examination, Dr. McMahon observed that Carroll was "extremely disorganized," "only partially oriented," and, in her clinical opinion, "experiencing both auditory and visual hallucinations." Dr. McMahon described the examination as "difficult" and concluded that, before further examination could occur, Carroll needed to be on an antipsychotic medication. She also told the jury she believed Carroll was psychoticand not malingeringat the time of the interview.
Dr. Danziger testified as to the same diagnoses that he provided in his written report to the court following his examination of Carroll in October 1991: (1) schizophrenia, chronic differentiated type, (2) alcoholism, and (3) multiple drug abuse. Dr. Danziger acknowledged the question of insanity at the time of the offense was "frankly a very difficult call" because there were no witnesses and Carroll had no recollection of the crime. Based upon witness statements, however, Dr. Danziger was able to opine Carroll "was psychotic both before and after the offense and, in fact, was quite grossly and bizarrely psychotic." Because of the psychosis, Dr. Danziger told the jury "it's my opinion that more likely than not [Carroll] was not responsible for his actions and was so psychotic he was unable to distinguish right from wrong." On cross-examination, Dr. Danziger admitted he still felt uncertain about his opinion, and he agreed with a statement in his written report that it was a close call"51% for and 49% against."
Dr. Benson was the final witness for the defense. As he did at the competency hearing, Dr. Benson explained his observations from his two examinations of Carroll. He informed the jury that, following the second examination, he had determined three diagnoses for Carroll: (1) "paranoid schizophrenia," (2) a "history of previous significant poly-substance abuse," and (3) "borderline intelligent quotient." With respect to the third diagnosis, Dr. Benson noted previous psychological tests had placed Carroll's IQ at 79, which was "absolutely below average IQ." Dr. Benson also provided an opinion as to Carroll's sanity at the time of the offense, testifying, "all in all, I think it is most likely that the defendant was actively psychotic at the time of the alleged crime, [and] therefore, did not know what he was doing or its consequences." On cross-examination, Dr. Benson acknowledged he was unable to form *1360 an opinion as to whether Carroll could distinguish between right and wrong.
The State called Dr. Kirkland as a rebuttal witness. Dr. Kirkland testified that, following psychological tests and examinations conducted at Florida Hospital in early December 1990, Dr. Kirkland could not make a "clear cut diagnosis" of Carroll. He noted, however, the testing indicated elements of depression, psychosis, and malingering. Although Dr. Kirkland explained he initially believed, prior to Carroll's stint at Florida Hospital, that he was not competent to stand trial, he reconsidered his opinion following an October 1991 examination and reported he thought Carroll was competent. Based upon that later examination, Dr. Kirkland diagnosed Carroll with antisocial personality, alcohol abuse, and a schizophrenia residual or chronic paranoid-type of personality disorder. Dr. Kirkland also testified he was initially unable to provide an opinion as to Carroll's mental condition at the time of the offense, but after reviewing investigative reports of the crime, he believed "if Mr. Carroll, in fact, did this crime that at the time, though he may have been intoxicated at the time, he knew what he was doing, knew the nature and consequences of it and knew that it was wrong."
Following three days of testimony, the jury convicted Carroll of both charges, and the trial moved into its penalty phase. During this proceeding, the defense argued "[t]he mitigators ... deal with his mental condition," but declined to call any witnesses because the doctors who "were able to render any type of relevant testimony as to his psychiatric condition at around the time of the offense have already testified and I don't want to open up the door to anything I've discussed with him." The defense did, however, submit an investigative report from 1969 indicating Carroll had been sexually molested as a child.
At the conclusion of the penalty phase, the jury returned a recommendation of death for the first-degree murder conviction by a vote of twelve to zero. Judge Perry followed the jury's recommendation and sentenced Carroll to death. He found three aggravating circumstances and no statutory mitigating factors, but concluded as a nonstatutory mitigating factor that Carroll suffered from "some possible mental abnormalities and has an antisocial personality."
On appeal to the Florida Supreme Court, Carroll raised five arguments, which included a claim that the trial court "failed to consider (or gave only little weight to) highly relevant and appropriate mitigating circumstances" during sentencing. In support of this claim, Carroll noted the extensive trial testimony regarding his mental health. He also maintained "[t]here was evidence ... presented that the defendant has a below normal intelligence, which is a factor in mitigation." The Florida Supreme Court affirmed Carroll's conviction and sentence. Carroll I, 636 So.2d at 1321. The United States Supreme Court denied Carroll's petition for writ of certiorari on October 31, 1994. Carroll v. Florida, 513 U.S. 973, 115 S.Ct. 447, 130 L.Ed.2d 357 (1994).

D. Carroll's First 3.850 Motion for Post-Conviction Relief
On February 1, 1996, Carroll filed his first motion to vacate judgment and sentence pursuant to Florida Rule of Criminal Procedure 3.850. He later submitted an amended motion, in which he raised 24 claims. Judge Perry again presided over the proceedings. Following a Huff[3] hearing, he concluded an evidentiary hearing *1361 was necessary on five of the claims, including Carroll's claims that his counsel was ineffective for failing to provide background materials to mental health experts to assist them in determining Carroll's insanity and intoxication at the time of the offense (Claim VI), that his counsel was ineffective for failing to provide background materials to mental health experts to assist them in determining Carroll's competency (Claim XIX), and that his counsel was ineffective for failing to properly investigate and provide the mental health experts with necessary information, thereby resulting in the loss of the affirmative defense of insanity (Claim XXI). On August 4-5, 1997, Judge Perry conducted an evidentiary hearing, during which five expert witnesses testified for the defense as to Carroll's mental health. Of these experts, threeDr. McMahon, Dr. Danziger, and Dr. Gutmantestified at the guilt phase of Carroll's trial.
Dr. Barry M. Crown, a psychologist who specialized in clinical and forensic psychology and neuropsychology, was the first health expert to testify. Dr. Crown had evaluated Carroll twice in 1997 and had conducted a number of neuropsychological tests during those meetings. The tests examined different facets of Carroll's intellectual functioning, including, "[i]n lay terms, how smart [Carroll] [wa]s, how well he deal[t] with difficulties," and "his intellectual efficiency." Based upon these tests, Dr. Crown testified Carroll's full scale IQ was 81 and described this score as being "in the border-line range, which is this nether nether land between mentally retarded and being low average."[4] He added the tests indicated Carroll had a problem-solving capacity "of someone who's 11 years and five months old" and had an attentional capacity "of someone who was about eighty years old suffering from the beginning of a degenerative process." Dr. Crown further testified regarding Carroll's general ability:
[H]is reading ability was at about the second grade level, spelling at about the third grade, simple arithmetic at about the fifth grade level. That's actually a range in the .08 percentile. That means that roughly better than 99 out of 100 people are able to process this better than he. And even at his best, 98 out of a hundred are able to function at a level that's significantly higher than he is.
Carroll's performance on the neuropsychological tests led Dr. Crown to conclude Carroll suffered from brain damage that affected his intellectual, cognitive, and affective capacities.
Dr. Crown further opined this brain damage had manifested early in Carroll's life, largely the result of fetal alcohol syndrome, physical abuse, and substance abuse. As support for this conclusion, Dr. Crown testified Carroll's brain capacity had not changed since he was a child, noting that Carroll's 1997 tests yielded similar results to those conducted when Carroll was twelve and thirteen years old. Specifically, Dr. Crown explained Carroll's childhood tests "produced the same numbers, the same scores that, that I [found]; they were in the same, same reference group with a minimal variance. And there's a great deal of similarity in terms of those identified functions." He noted Carroll produced a full-scale IQ of 80 on the Weschler Intelligence Scale for Children in both 1968 and 1969, and testified "it's highly unlikely that someone could fake that number on a deliberate basis beginning when they were 12 years old." Dr. Crown did mention a 1990 test had yielded a verbal IQ of 58 but explained the score was a lower outlier because Carroll was psychotic at the time of the test.
*1362 Dr. Crown concluded his testimony on direct examination by stating if he had been given the opportunity to conduct the testing in 1992 and to testify at Carroll's trial, he would have testified Carroll met the requirements for two statutory mitigating factorsspecifically, Carroll's capacity to appreciate the criminality of his conduct and conform his conduct to the requirements of the law was substantially impaired, and Carroll committed the murder under the influence of extreme mental or emotional disturbance.
Like Dr. Crown, Dr. Jethro W. Toomer, a forensic psychologist, was a new mental health expert for the defense. Dr. Toomer stated he conducted a psychological evaluation of Carroll on January 25, 1996, at the request of Carroll's counsel. After examining Carroll and reviewing his medical records, Dr. Toomer believed Carroll "present[ed] symptomatology that r[an] the entire gamut of several personality disorders, all the way through to a major mental disorder. At times he manifest[ed] symptomatology indicative of psychosis... and at other times he manifest[ed] symptomatology reflecting a severe personality disorder." Dr. Toomer further testified Carroll's mental history was inconsistent with a conclusion that he was malingering at the time of trial. Based upon these conclusions, he stated that had he been called during Carroll's penalty phase, he would have testified Carroll was unable to appreciate the criminality of his conduct and suffered from severe mental or emotional disturbance.
Dr. McMahon and Dr. Danziger again testified for the defense and reiterated their initial conclusions as to Carroll's mental status and competency. Like Dr. Crown and Dr. Toomer, they both testified that if they would have been called during the penalty phase of Carroll's trial proceedings, they would have opined that Carroll's capacity to appreciate the criminality of his conduct and conform his conduct to the requirements of the law was substantially impaired, and that he committed the murder under the influence of extreme mental or emotional disturbance.
Dr. Gutman was the final mental health expert to testify at the evidentiary hearing on Carroll's 3.850 motion. Dr. Gutman had testified for the State at trial, but had changed his diagnosis after reviewing Carroll's entire medical history and psychological evaluations. After initially concluding Carroll had psychosexual and mixed personality disorders and was malingering during his September 1991 evaluation, Dr. Gutman amended his diagnosis to include brain damage: "My current diagnosis would be mental disorder with mood, memory, personality change and cognitive decline associated with alcohol deterioration and influence on the brain."[5] Dr. Gutman explained the portions of Carroll's history that led to his new diagnosis, including school records that indicated Carroll's IQ was "in the 75 to 85 range." Dr. Gutman further testified that had he been called during Carroll's penalty phase, he would have given an opinion that Carroll was unable to appreciate the criminality of his conduct and suffered from severe mental or emotional disturbance.
On October 20, 1998, Judge Perry entered an order denying all of Carroll's claims for post-conviction relief. The Florida Supreme Court later affirmed the trial court's order and denied Carroll's petition for a writ of habeas corpus. Carroll II, 815 So.2d at 607.


*1363 E. Carroll's Successive 3.850 Motion

On April 22, 2003, Carroll filed a successive 3.850 motion, raising two new claims based upon the Supreme Court's decisions in Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), and Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). With respect to his Atkins claim, Carroll argued he was exempt from execution under the Eighth Amendment because he was "borderline mentally retarded and/or suffering from such severe brain damage and mental limitations that death could never be an appropriate punishment."
Judge Perry, who had presided over Carroll's trial in 1992 and his initial post-conviction proceedings in 1997, once again was assigned the case and, on June 12, 2003, held a Huff hearing on Carroll's new claims. At that hearing, Carroll's collateral counsel maintained Carroll had made a prima facie showing of mental retardation to warrant an evidentiary hearing under Atkins: "It's our contention he has substantial limitation of present functioning. IQ range from 75 to 81. Postconviction and trial record demonstrate he also suffers from other mental illness, comparative reasoning." As support for this argument, collateral counsel relied solely on existing evidence in the record and did not proffer any additional evidence regarding Carroll's mental retardation.[6] Specifically, collateral counsel cited Dr. Crown's testimony regarding Carroll's IQ and intellectual ability from the evidentiary hearing on Carroll's initial 3.850 motion. He also pointed to evidence in the record pertaining to Carroll's reading, spelling, and arithmetic abilities as well as his poor performance in school, contending Carroll's learning disabilities evidenced a significant limitation in adaptive functioning. Collateral counsel further argued Carroll had exhibited problems with self-direction and self-care during his life. He concluded by noting Carroll's deficits in adaptive behavior manifested by age eighteen.
On January 12, 2004, the trial court summarily denied Carroll's successive 3.850 motion. With respect to Carroll's Atkins claim, Judge Perry considered the evidence presented at trial, the prior evidentiary hearing on Carroll's first 3.850 motion, and the Huff hearing on his successive motionall proceedings over which Judge Perry had presidedand concluded "Defendant does not meet the definition of mentally retarded as set forth in Atkins because his IQ score is and was over 75." He also found the record showed no significant limitation in Carroll's adaptive skills. Accordingly, Judge Perry denied Carroll's mental retardation claim. Furthermore, he declined to apply Atkins to the mentally ill, noting "the eighth amendment of the United States Constitution prohibits the execution of insane prisoners and there are already numerous safeguards in place for the protection of the truly insane." On May 12, 2005, the Florida Supreme Court affirmed without an opinion. Carroll v. State, 904 So.2d 430 (Fla.2005) (Carroll III).


*1364 F. Carroll's § 2254 Petition

On June 8, 2005, Carroll filed a petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254 with the United States District Court for the Middle District of Florida, raising seven claims for relief. Without conducting an evidentiary hearing, the district court denied Carroll's petition. The bulk of the district court's order addressed Carroll's Atkins claim. Regarding Carroll's mental capacity, the district court concluded "the record supports the trial court's finding that Petitioner's IQ is over 75, and Petitioner has failed to rebut this finding by clear and convincing evidence." Interpreting Atkins to apply only to persons who possess IQs of 75 or lower, the district court determined the state trial court's decision that Carroll was not entitled to relief was not "contrary to" or "an unreasonable application of" clearly established federal law and "was not unreasonable in light of the substantial evidence supporting its conclusion." Furthermore, the district court declined to extend Atkins to the mentally ill and thus denied Carroll's equal protection claim as well. Carroll filed a notice of appeal with this Court, and the district court granted a COA as to Carroll's Atkins claim. This Court later denied Carroll's request to expand the COA to cover additional issues.

II. STANDARD OF REVIEW
Following a district court's denial of a habeas petition, this Court reviews questions of law and mixed questions of law and fact de novo and findings of fact for clear error. Nyland v. Moore, 216 F.3d 1264, 1266 (11th Cir.2000) (per curiam).
Carroll filed his federal habeas petition after April 24, 1996, and thus this case is governed by the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), which "establishes a highly deferential standard for reviewing state court judgments." Parker v. Sec'y for Dep't of Corr., 331 F.3d 764, 768 (11th Cir.2003). Under AEDPA, a federal court shall not grant habeas relief on claims that were previously adjudicated in state court unless the state court's decision was (1) "contrary to, or involved an unreasonable application of, clearly established Federal law as determined by the Supreme Court of the United States; or (2) ... 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).

III. DISCUSSION
Carroll essentially asserts two Atkins claims in his § 2254 petition. First, he maintains that he is "functionally mentally retarded," a status that exempts him from execution under Atkins, and that the state court's denial of his request for an evidentiary hearing as to this issue violated his due process rights. Second, he contends the state trial court's decision not to extend Atkins to the mentally ill violated his equal protection rights because the mentally ill are similarly situated to the mentally retarded and the rationale behind Atkins applies equally to persons with mental illnesses.

A. Due ProcessMental Retardation
Carroll argues his due process rights were violated when the state court failed to grant an evidentiary hearing on his claim of mental retardation under Atkins. Carroll asserts the records on which the state trial court relied to determine he did not meet the definition of mental retardation under Atkins were incomplete, inconsistent, and analyzed outside the context of a mental retardation hearing. He further contends the record suggests his IQ may be less than 75, and an evidentiary hearing is necessary to conclusively establish his *1365 level of intellectual functioning and adaptive behavior.
Carroll conflates a number of issues in his due process argument, and we believe separating these issues provides clarity in determining both the appropriate legal analysis and the appropriate remedy. We thus construe Carroll's briefs and oral argument as advocating three separate bases of relief: (1) Carroll is entitled to habeas corpus relief because the state court violated his due process rights by failing to grant an evidentiary hearing on his Atkins claim, (2) Carroll is entitled to habeas corpus relief because he is mentally retarded and thus exempt from execution under Atkins, and (3) Carroll is entitled to an evidentiary hearing on his Atkins claim, and we should remand this case to the district court to conduct one.
We consider these issues in turn.

1. Whether the state trial court violated Carroll's due process rights when it declined to grant him an evidentiary hearing on his claim of mental retardation.
Carroll contends the state trial court violated his due process rights when it summarily denied his Atkins claim of mental retardation without an evidentiary hearing. He maintains Florida law required the state court to conduct an evidentiary hearing on his successive post-conviction motion because the claim was legally sufficient under Atkins and not conclusively refuted by the record. Carroll also insinuates federal law (i.e., Atkins itself), in addition to Florida law, mandated that the state court conduct an evidentiary hearing in this case.
This Court has repeatedly held defects in state collateral proceedings do not provide a basis for habeas relief. See, e.g., Anderson v. Sec'y for Dep't of Corr., 462 F.3d 1319, 1330 (11th Cir.2006) (per curiam); Quince v. Crosby, 360 F.3d 1259, 1262 (11th Cir.2004); Spradley v. Dugger, 825 F.2d 1566, 1568 (11th Cir.1987) (per curiam). The reasoning behind this well-established principle is straightforward: a challenge to a state collateral proceeding does not undermine the legality of the detention or imprisonmenti.e., the conviction itselfand thus habeas relief is not an appropriate remedy. See Quince, 360 F.3d at 1261-62; Spradley, 825 F.2d at 1568. Moreover, such challenges often involve claims under state lawfor example, Florida Rules of Criminal Procedure 3.850 and 3.851, which govern the availability of, and procedures attendant to, post-conviction proceedings in Floridaand "[a] state's interpretation of its own laws or rules provides no basis for federal habeas corpus relief, since no question of a constitutional nature is involved." See McCullough v. Singletary, 967 F.2d 530, 535 (11th Cir.1992).
Because of this bar to relief, we have stated it is "beyond debate" that a state court's failure to conduct an evidentiary hearing on a post-conviction motion does not constitute a cognizable claim for habeas relief. See Anderson, 462 F.3d at 1330. In Spradley, we considered a habeas petition in which a Florida inmate claimed "the state trial court which heard and denied his 3.850 motion violated his due process rights because it failed to conduct an evidentiary hearing and did not attach to its opinion denying relief those portions of the record on which it relied." 825 F.2d at 1567. We rejected this claim, holding a state court's failure to conduct an evidentiary hearing cannot form the basis for habeas relief because such an error does not "undermine[ ] the validity of petitioner's conviction" and is "unrelated to the cause of petitioner's detention." Id. at 1568. We later reaffirmed this general principle in Quince, noting "an alleged defect in a collateral proceeding does not state a basis for habeas relief." 360 F.3d at 1262.
*1366 Under this Court's precedent, Carroll's claim that the state court violated his due process rights by failing to conduct an evidentiary hearing under Florida Rule of Criminal Procedure 3.850 and 3.851 on his post-conviction Atkins claim does not state a claim on which this Court may grant habeas relief. See Spradley, 825 F.2d at 1568. Carroll does not address this bar to relief. Accordingly, we deny Carroll's due process claim for habeas relief to the extent it rests on the state court's failure to grant an evidentiary hearing under Florida law.
Carroll has also suggested the Atkins decision itself compels state courts to conduct evidentiary hearings on claims of mental retardation. Atkins, however, simply sets forth the constitutional prohibition on the execution of mentally retarded individuals, and it specifically "leave[s] to the States the task of developing appropriate ways to enforce the constitutional restriction," Atkins, 536 U.S. at 317, 122 S.Ct. at 2250, which presumably includes the availability of, and procedures attendant to, evidentiary hearings before state trial courts, see Fla. R. Crim P. 3.203(e), 3.850(d), 3.851(f)(5)(A)-(B). Carroll points to no language in Atkins, or any other decision of the Supreme Court or this Court, to support his argument that federal law requires state courts to conduct evidentiary hearings on every claim of mental retardationespecially in cases, such as Carroll's, in which a petitioner has presented evidence regarding his mental health in three prior proceedings. Finding no case to support Carroll's argument ourselves, we conclude his due process claim regarding the failure of the state court to conduct an evidentiary hearing does not state a cognizable claim for habeas relief.[7]


2. Whether Carroll is exempt from execution under Atkins because he is mentally retarded.

Carroll maintains he is mentally retarded and thus exempt from execution under Atkins. As evidence of his mental retardation, Carroll notes he has scored less than 75 on several IQ tests; his reading ability is at the second-grade level, his spelling ability is at the third-grade level, and his arithmetic ability is at the fifth-grade level; and he exhibited poor adaptive behavior in his childhood and adolescence.
In Atkins, the Supreme Court held the execution of mentally retarded individuals violated the Eighth Amendment's prohibition against cruel and unusual punishments. 536 U.S. at 321, 122 S.Ct. at 2252. Although the Court left "to the States the task of developing appropriate ways to enforce the constitutional restriction," id. at 317, 122 S.Ct. at 2250, it reproduced definitions of mental retardation formulated by the American Association on Mental Retardation and American Psychiatric Association:
The American Association on Mental Retardation (AAMR) defines mental retardation as follows: "Mental retardation refers to substantial limitations in present functioning. It is characterized by significantly subaverage intellectual functioning, existing concurrently with related limitations in two or more of the following applicable adaptive skill areas: communication, self-care, home living, social skills, community use, self-direction, health and safety, functional academics, leisure, and work. Mental retardation manifests before age 18."

*1367 The American Psychiatric Association's definition is similar: "The essential feature of Mental Retardation is significantly subaverage general intellectual functioning (Criterion A) that is accompanied by significant limitations in adaptive functioning in at least two of the following skill areas: communication, self-care, home living, social/interpersonal skills, use of community resources, self-direction, functional academic skills, work, leisure, health, and safety (Criterion B). The onset must occur before age 18 years (Criterion C)."
Id. at 308 n. 3, 122 S.Ct. at 2245 n. 3 (internal citations and emphasis omitted). The Court also noted that "`[m]ild' mental retardation is typically used to describe people with an IQ level of 50-55 to approximately 70," id., and that an IQ score between 70 and 75 "is typically considered the cutoff IQ score for the intellectual function prong of the mental retardation definition," id. at 309 n. 5, 122 S.Ct. at 2245 n. 5.
When Atkins was decided in 2002, the state of Florida already had a law prohibiting the execution of mentally retarded individuals. See Fla. Stat. § 921.137. That law defines "mental retardation" as "significantly subaverage general intellectual functioning existing concurrently with deficits in adaptive behavior and manifested during the period from conception to age 18." The statute further defines "significantly subaverage general intellectual functioning" as "performance that is two or more standard deviations from the mean score on a standardized intelligence test." The Florida Supreme Court has interpreted this definition as requiring a petitioner to establish he has an IQ of 70 or below. See Jones v. State, 966 So.2d 319, 329 (Fla.2007). Section 921.137, however, applies only to persons sentenced to death after the effective date of the statute in 2001. Fla. Stat. § 921.137(8). Thus, as the district court noted, § 921.137 is inapplicable to Carroll, and "it is only within the context of Atkins' mental retardation definition that this Court evaluates Petitioner's claim."
The state trial court made factual determinations that Carroll is not mentally retarded and that he possesses an IQ of above 75. In challenging these determinations, Carroll points to evidence in the record indicating he has scored below 75 on previous IQ tests. Specifically, he notes the trial testimony of Dr. Michael Gutman, who testified "psychological tests showed [Carroll] to have an IQ of sixty or in the sixty to sixty-nine range." Carroll also states he scored a 58 on an IQ test shortly after being arrested. With respect to his adaptive behavior, Carroll emphasizes his poor cognitive abilities, citing the testimony of Dr. Barry Crown and Dr. Elizabeth McMahon at the evidentiary hearing on his initial post-conviction motion, as well as adolescent behavioral problems, citing an affidavit of Nelly T. Smith, his sister.
This evidence fails to undermine the state court's factual determinations or establish those determinations were unreasonable in light of the evidence before the state trial court. See 28 U.S.C. § 2254(d)(2). The record in this case is replete with evidencepresented at three separate proceedings, two of which were before the same state trial judgesupporting the state court's findings. (See R2-20, Exh. Vol. 4 at 511-12[8] (Dr. Gutman's *1368 testimony that Carroll was "in the high average range of intelligence" and his IQ was between 105 and 110); R2-20 Exh. Vol. 4 at 512 (IQ tests on which Carroll had scored in the high 70s and low 80s); R2-20, Exh. Vol. 6 at 758 (school IQ test of 79); R2-20, Exh. Vol. 10 at 1059 (Dr. Gutman's report indicating Carroll was "of average to high average intelligence"); R2-20, Exh. Vol. 10 at 1064 (Dr. Benson's report indicating Carroll had a borderline IQ); R2-20, Exh. Vol. 10 at 1070 (Dr. Danziger's report describing Carroll's intellect as "roughly in the average to below average range"); R2-20, Exh. PC Vol. 2 at 229 (Dr. Crown's testimony that Carroll's IQ was 81, which was in a "nether nether land between mentally retarded and being low average"); R2-20, Exh. PC Vol. 2 at 229 (tests scores showing a verbal IQ of 84 and a performance IQ of 79); R2-20, Exh. PC Vol. 2 at 237-38 (school IQ tests of 80); R2-20, Exh. PC Vol. 2 at 392 (school records indicating Carroll's IQ ranged from 80 to in the 75-to-85 range).) In addition to the facts in the record, Carroll's counsel admitted at the state Huff hearing that Carroll had an "IQ range from 75 to 81."[9] (See R2-20, Exh. PC2 Vol. 1 at 23.)
Moreover, the state court considered the same evidence Carroll has presented in his briefs to this Court and found it unpersuasive. Indeed, Carroll does not provide the full context of the testimony regarding his sub-75 IQ scores: the same expert, Dr. Gutman, who testified at trial as to tests showing an IQ in the 60-to-69 range also estimated Carroll's IQ to be between 105 and 110, and Carroll's own expert at the evidentiary hearing on his initial 3.850 motion maintained Carroll's previous IQ score of 58 was likely the result of psychosis.
Finally, Carroll has never attempted to proffer any additional evidence to any courtwhether it be the state courts, the district court, or this Courtthat would undermine the exhaustive evidence already in the record indicating he is not mentally retarded. Quite simply, Carroll has had numerous opportunities (i.e., his competency hearing, his trial, and the evidentiary hearing on his initial 3.850 motion) during the past eighteen years to present evidence supporting a finding of mental retardation.[10] The state trial court judge, who presided over both Carroll's trial and evidentiary hearing on his initial 3.850 motion and was intimately aware of the evidence presented during these proceedings, found he had failed to do so, and the record supports this finding.
Our review does not stop here, however, because Carroll also maintains the state court construed Atkins too narrowly, and thus its decision is "contrary to" or "an unreasonable application" of clearly established federal law. He maintains Atkins does not require individuals to possess a certain IQ (i.e., below 75) to satisfy the definition of mental retardation. He further asserts the intellectual functioning prong of the mental retardation inquiry is "interrelated" with the adaptive behavior prong. Thus, according to Carroll, a borderline IQ, accompanied by a serious mental illness that substantially impairs an individual's cognitive abilities, can satisfy the definition of mental retardation in *1369 some circumstances. He asserts his case is one such circumstance.
As the district court noted, the mental health experts who have evaluated Carroll have diagnosed him with a myriad of mental disorders, including schizophrenia, psychosis, fetal alcohol syndrome, brain damage, psychosexual disorder, and personality disorder. Although some evidence in the record suggests Carroll malingered during his examinations, we do not doubt Carroll indeed suffers from some, if not multiple, forms of mental illness. That said, the mental retardation inquiry is not different merely because an individual suffers from mental illness. The inquiry still requires an individual to demonstrate "significantly subaverage general intellectual functioning" along with deficits in adaptive behavior and an onset before age 18. In other words, contrary to Carroll's assertions, the intellectual functioning and adaptive behavior prongs must each be satisfied for an individual to qualify as mentally retarded. See Atkins, 536 U.S. at 308 n. 3, 122 S.Ct. at 2245 n. 3 (reproducing the American Association on Mental Retardation's and the American Psychiatric Association's definitions of mental retardation, which both state the three-criteria test for mental retardation in the conjunctive); see also Fla. Stat. § 921.137 (stating significantly subaverage general intellectual functioning must exist concurrently with deficits in adaptive behavior).
Carroll further asserts his mental illness can render him "functionally mentally retarded," as was apparently the case when a psychotic episode caused him to perform poorly on an IQ test shortly after his arrest. Under Carroll's interpretation of Atkins, "the functionally mentally retarded" are also exempt from execution. We reject this argument for the same reasons articulated by the district court. Atkins protects only those individuals who are mentally retarded, as is evident by the third prong of the mental retardation inquiry, which requires onset by age 18. See id., 122 S.Ct. at 2245 n. 3; see also Fla. Stat. § 921.137. Thus, a constitutional rule exempting the "functionally mentally retarded" from execution would go beyond the holding of Atkins, something this Court may not do when reviewing § 2254 petitions. See 28 U.S.C. § 2254(d)(1); see also infra III.B.
In sum, we conclude the state court's factual determination that Carroll is not mentally retarded was reasonable and thus Carroll has failed to demonstrate the state court's denial of his Atkins claim "was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." See 28 U.S.C. § 2254(d)(2). We also hold the state trial court reasonably applied the controlling Supreme Court precedent (Atkins) and thus its decision was not "contrary to" or "an unreasonable application of" clearly established federal law. See 28 U.S.C. § 2254(d)(1). Accordingly, we deny this claim.

3. Whether this case should be remanded for the district court to conduct an evidentiary hearing.
Carroll alternatively argues this Court should remand his Atkins claim to the district court for an evidentiary hearing to determine his mental capacity. The Supreme Court has held federal courts must take into account the deferential standards prescribed by AEDPA in determining whether an evidentiary hearing is appropriate. See Schriro v. Landrigan, 550 U.S. 465, 474, 127 S.Ct. 1933, 1940, 167 L.Ed.2d 836 (2007). "It follows that if the record refutes the applicant's factual allegations or otherwise precludes habeas relief, a district court is not required to hold an evidentiary hearing." Id. at 474, 127 S.Ct. at 1940. In this case, the factual *1370 record is sufficient for this Court to conclude the state court's adjudication was not "contrary to" or "an unreasonable application of" clearly established federal law or "based on an unreasonable determination of the facts." See supra III.A.2. Ample evidence, in the form of exhaustive expert testimony from Carroll's competency hearing, trial, and initial post-conviction evidentiary hearing, supports the state court's determination that he is not mentally retarded. Accordingly, an evidentiary hearing on Carroll's Atkins claim is unnecessary.[11]

B. Equal ProtectionMental Illness
In addition to his mental retardation claims, Carroll maintains he is also exempt from execution because he is mentally ill. He maintains the rationale behind the Supreme Court's decision in Atkins applies equally to persons "who are unable to control their conduct due to mental illness." Specifically, he notes mentally ill persons, like the mentally retarded, act with a lesser moral culpability, and this lesser culpability does not merit retribution in the form of the death penalty. Carroll also asserts executing mentally ill persons does not further the goal of deterrence because, like the mentally retarded, the mentally ill cannot process the possibility of execution as a penalty and control their conduct based on that information. Carroll argues the state court's failure to apply Atkins to the mentally ill was a violation of his right to equal protection.
Atkins did not explicitly address the suitability of capital punishment within the context of mentally ill individuals. Carroll, however, requests this Court extend Atkins to prohibit the execution of the mentally ill. Such an extension would constitute a new rule of constitutional law. See Spaziano v. Singletary, 36 F.3d 1028, 1042 (11th Cir.1994) ("Even if the result the habeas petitioner seeks is within the logical compass of a prior Supreme Court decision; even if prior Supreme Court decisions inform, or even control or govern, the analysis of the claim; it is still a new rule claim unless the rule is actually dictated by pre-existing precedent." (internal citations and quotation marks omitted)). Under AEDPA, however, this Court cannot create new rules of constitutional law within the context of a habeas petition by a state prisoner. See 28 U.S.C. § 2254(d)(1) (stating a federal court may not grant habeas relief to a state prisoner unless the adjudication of his claim in state court "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" (emphasis added)). Accordingly, sans a decision from the Supreme Court barring the execution of mentally ill prisoners, we reject Carroll's claim that he is exempt from execution because he is mentally ill.

IV. CONCLUSION
Carroll has failed to demonstrate the state court's conclusion that he was not entitled to relief under Atkins was "contrary to" or "an unreasonable application of" clearly established federal law or "based on an unreasonable determination of the facts." See 28 U.S.C. § 2254(d). Accordingly, we affirm the district court's denial of his § 2254 petition.
AFFIRMED.
NOTES
[1]  Dr. Lawrence B. Erlich did not appear at the hearing and did not examine Carroll following the court's order in August 1991. Dr. Erlich, a forensic psychiatrist, did evaluate Carroll on December 7, 1990, at which time he supplied a report to the court indicating he believed Carroll was competent to stand trial.
[2]  Carroll claimed to have no memory of the sexual assault and murder of Christine McGowan.
[3]  Huff v. State, 622 So.2d 982 (Fla. 1993).
[4]  Dr. Crown also placed Carroll's verbal IQ at 84 and his performance IQ at 79.
[5]  This new diagnosis, however, did not alter Dr. Gutman's initial diagnoses of psychosexual and mixed personality disorders and malingering, which he still maintained at the time of the post-conviction evidentiary hearing. Those traits were still present, with Carroll's brain damage explaining why he possessed them.
[6]  In his briefs to this Court, Carroll states, without citation to the record, that he proffered a recent IQ score of 75 to the state court. We have found nothing in the record supporting this statement. At the Huff hearing, Carroll's counsel did maintain Carroll had posted an IQ score of 75, but counsel made this statement in his reply to the State's argument and did not provide any further information regarding this score, including whether it was the result of recent testing. Likewise, Carroll's successive 3.850 motion does state he "has been measured with a full scale IQ at 75." This number, however, appears to be an average of several previous IQ scores; the successive 3.850 motion does not mention any recent testing. Indeed, at oral argument, Carroll's counsel conceded no new evidence was proffered to the state court.
[7]  Although not a basis for our holding on this issue, we again note Carroll did not proffer any new evidence regarding his mental retardation claim before the state court at the Huff hearing. Rather, the evidence he proffered was limited to testimony and affidavits from the evidentiary hearing on his initial 3.850 motion.
[8]  The state court filings were filed with the district court as an exhibit to R2-20 and consist of three sets of volumes. One set of volumes contains the record from Carroll's trial and direct appeal; these volumes are designated as "Vol." Another set of volumes contains the record regarding Carroll's first 3.850 motion for post-conviction relief; these volumes are designated as "PC Vol." The final set of volumes contains the record regarding Carroll's successive 3.850 motion for post-conviction relief; these volumes are designated as "PC2 Vol."
[9]  Counsel's argument at the Huff hearing, however, was consistent with the claim in Carroll's successive 3.850 motionthat is, Carroll is borderline mentally retarded.
[10]  Although Atkins was not decided until 2002, mental retardation has long been considered a mitigating circumstance under Florida law. See Crook v. State, 813 So.2d 68, 77 n. 7 (Fla.2002) (listing cases).
[11]  Although Carroll did not explicitly raise the argument, we conclude, for the same reasons, the district court did not abuse its discretion in disposing of Carroll's § 2254 petition without conducting an evidentiary hearing.
