
641 F.3d 1276 (2011)
Norberto PIETRI, Petitioner-Appellant,
v.
FLORIDA DEPARTMENT OF CORRECTIONS, Secretary of Florida Department of Corrections, Florida Attorney General, Respondents-Appellees.
No. 09-11750.
United States Court of Appeals, Eleventh Circuit.
May 25, 2011.
*1278 William M. Hennis, III, Capital Collateral Regional CounselSouth, Ft. Lauderdale, FL, for Petitioner-Appellant.
Leslie T. Campbell, West Palm Beach, FL, for Respondents-Appellees.
Before DUBINA, Chief Judge, and CARNES and BLACK, Circuit Judges.
DUBINA, Chief Judge:
Petitioner, Norberto Pietri ("Pietri"), appeals the district court's order denying him habeas relief pursuant to 28 U.S.C. § 2254. For the reasons that follow, we affirm.

I. BACKGROUND

A. Facts

The facts are taken verbatim from the Supreme Court of Florida's opinion addressing Pietri's appeal of his convictions and sentences.
On August 18, 1988, Pietri walked away from the Lantana Community Correctional Work Release Center. At the time, he was restricted to the center's grounds while he awaited transfer to a more secure facility. After his escape, Pietri began a four-day binge of using cocaine. He testified that during this time he committed burglaries to support his drug use. On August 22, he ran out of drugs.
Driving a pickup truck he had stolen the day before, Pietri went to a house, broke in, and stole items including a 9-mm semiautomatic firearm and a .38-caliber revolver. After the burglary, a witness saw Officer Chappell sitting on his motorcycle, apparently watching for speeding motorists. The witness saw a man driving a silver pickup truck speed by Chappell, and the officer gave chase. The driver stopped after about a mile. Chappell motioned for the driver to move forward to avoid blocking traffic, and the driver complied.
Witnesses testified that as Chappell approached the truck, his gun was in its holster. When the officer was within two to four feet of the truck the driver shot him once in the chest. A forensics firearm examiner testified that Chappell was shot from a distance of three to eight feet. He testified that the casing of the bullet that killed Chappell matched the casings of 9-mm bullets provided by the burglary victim. Thus, the firearms examiner concluded, the bullets had been fired from a weapon taken in the burglary.
After firing the gun, the driver sped off, and Chappell radioed that he had been shot. The first officer who arrived at the scene testified that Chappell's gun was still in the holster. The holster had been unsnapped, however, indicating that Chappell may have tried to remove his weapon.
After leaving the scene of the shooting, the driver went to his nephew's house for help disposing of the truck. He dumped the truck in a canal off the Florida Turnpike, and a fingerprint found inside the driver's side window was later identified as Pietri's. Officer Chappell's death prompted an intense search, with Pietri identified as the prime suspect. Pietri stole another car on August 24 and was spotted by police officers near his sister's apartment and later by an off-duty officer at a church. Pietri threatened to shoot the officer, who was not in uniform, and escaped.
Later that same evening, a couple and their five-year-old son were in their car in the driveway of their home. As they prepared to leave, the husband realized he had left something in the house. When he returned to the house, Pietri got in the car and told the wife, "We're *1279 leaving, we're leaving." He told the woman, who was in the driver's seat, "Drive, or I'll shoot you." When she hesitated, Pietri pushed her out of the car and began to drive away. He slowed down, however, and let the husband, who had emerged from the house, take their son from the back seat.
Another police officer spotted the couple's car. The driver stopped and waved the officer toward the car. As the officer approached the car with his gun drawn, the driver sped off. Two other officers picked up the chase, which proceeded at speeds of more than 100 miles per hour. Pietri eventually lost control of the car, then jumped out of the car and began running. As Pietri ran, he reached into his pants, pulled out a bag of cocaine, and put it into his mouth. Delray Beach officer Michael Swigert caught Pietri and arrested him.
Pietri testified in his own defense that he is blind in his right eye and that he developed a cocaine addiction which he financed with burglaries. He testified that Chappell stopped him while he was planning to sell stolen goods. Pietri admitted shooting Chappell, but said he had not planned to kill the officer and did not aim for his heart.
Pietri v. State, 644 So.2d 1347, 1350 (Fla. 1994).

B. Procedural History

A jury convicted Pietri of first degree murder of police officer Brian Chappell and numerous other felonies. The jury recommended, by a vote of 8 to 4, that Pietri receive a death sentence for the murder conviction. The trial court followed the jury's recommendation and imposed a death sentence. The Florida Supreme Court affirmed Pietri's convictions and sentences on appeal, Pietri v. State, 644 So.2d 1347 (Fla.1994), and the United States Supreme Court denied certiorari, Pietri v. Florida, 515 U.S. 1147, 115 S.Ct. 2588, 132 L.Ed.2d 836 (1995). Pursuant to Florida Rules of Criminal Procedure Rule 3.850, Pietri filed a motion for post-conviction relief on March 14, 1997, and the trial court granted him an evidentiary hearing on his claims of ineffective assistance of guilt and penalty phase counsel. Following the hearing, the trial court denied Pietri collateral relief. Pietri appealed to the Florida Supreme Court and simultaneously filed a petition for writ of habeas corpus in the Florida Supreme Court. The state appellate court affirmed the trial court's order denying Pietri collateral relief, and it denied his petition for writ of habeas corpus. Pietri v. State, 885 So.2d 245, 276 (Fla.2004). Pietri then filed a federal habeas petition, which the district court denied. Pietri filed an application for a certificate of appealability ("COA"), which the district court granted.

II. ISSUES
1. Whether the district court properly denied Pietri relief on his claims of ineffective assistance of counsel at the guilt phase.
2. Whether the district court properly denied Pietri relief on his claim that counsel failed to investigate and present more detailed mitigation evidence at the penalty phase.
3. Whether the district court properly determined that Pietri's claim of ineffective assistance of appellate counsel for failure to challenge the trial court's impartiality was barred from federal review.

III. STANDARDS OF REVIEW
"When reviewing the district court's denial of a habeas petition, we review 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). Under *1280 the Anti-terrorism and Effective Death Penalty Act ("AEDPA"), "our review is greatly circumscribed and is highly deferential to the state courts." Crawford v. Head, 311 F.3d 1288, 1295 (11th Cir. 2002). We presume that state court factual findings are correct unless the petitioner rebuts that presumption by clear and convincing evidence. 28 U.S.C. § 2254(e)(1). A federal court may not grant habeas relief unless the decision of the state court either was "contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States [or] was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." Id. § 2254(d). The petitioner must show that the state court applied federal law to the facts of his case in an objectively unreasonable manner. Woodford v. Visciotti, 537 U.S. 19, 25, 123 S.Ct. 357, 360, 154 L.Ed.2d 279 (2002). "[A]n unreasonable application of federal law is different from an incorrect application of federal law." Williams v. Taylor, 529 U.S. 362, 410, 120 S.Ct. 1495, 1522, 146 L.Ed.2d 389 (2000).
"An ineffective assistance of counsel claim is a mixed question of law and fact that the court reviews de novo." Jones v. Campbell, 436 F.3d 1285, 1292 (11th Cir.2006). To establish a claim of ineffective assistance of counsel, the petitioner must establish that (1) "counsel's representation fell below an objective standard of reasonableness" and (2) "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland v. Washington, 466 U.S. 668, 688, 694, 104 S.Ct. 2052, 2064, 2068, 80 L.Ed.2d 674 (1984). In Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), the Supreme Court reiterated that the clearly established federal precedent for evaluating ineffective assistance of counsel claims is found in Strickland. Id. at 521, 123 S.Ct. at 2535. The Court further noted:
[W]e emphasize that Strickland does not require counsel to investigate every conceivable line of mitigating evidence no matter how unlikely the effort would be to assist the defendant at sentencing. Nor does Strickland require defense counsel to present mitigating evidence at sentencing in every case.... We base our conclusion on the much more limited principle that "strategic choices made after less than complete investigation are reasonable" only to the extent that "reasonable professional judgments support the limitations on investigation." A decision not to investigate thus "must be directly assessed for reasonableness in all the circumstances."
Id. at 533, 123 S.Ct. at 2541 (quoting Strickland, 466 U.S. at 689-91, 104 S.Ct. at 2065-66).
We review de novo the district court's determination that Pietri's claim of ineffective assistance of appellate counsel is barred from federal habeas review because it was not properly exhausted. See Mize v. Hall, 532 F.3d 1184, 1190 (11th Cir.2008).

IV. DISCUSSION

A. Ineffective Assistance of Counsel at the Guilt Stage

Pietri contends that his trial counsel, Peter Birch and Donnie Murrell, were ineffective because they failed to investigate and proffer an intoxication defense based on his extensive drug use that would have shown that he did not have the requisite intent to commit first degree murder. Pietri raised this claim in his post-conviction motion, and the trial court denied relief after an evidentiary hearing.
During the hearing, Pietri proffered evidence from several expert witnesses regarding *1281 his alleged intoxication. Dr. Jonathan Lipman, a neuropharmacologist[1], testified that he could speak about Pietri's state of mind only in neuropharmalogical terms. (R. Vol. 49, p. 1032; Vol. 50, p. 1105.) Dr. Lipman opined that at the time of the crime, cocaine toxicity was still present in Pietri's bloodstream, meaning that Pietri still craved the drug and was going through a withdrawal process at the time of the shooting. (R. Vol. 50, p. 1009-1010.) Dr. Lipman concluded that Pietri was suffering from "metabolic intoxication" which means that he had poor impulse control and his brain chemistry was not normal. (Id. at 1113.) Dr. Lipman testified that the evidence was consistent with an impulsive act, not a specific intent to perform the act. (Id. at 1116.)
Dr. Harry Krop, a clinical psychologist, testified at the hearing that he reviewed several doctors' depositions, the police interview, the trial court's order, Dr. Iodice's testimony, Dr. Caddy's penalty-phase testimony, the medical examiner's deposition, the correctional facility's psychological screening report, and Dr. Goldberg's deposition. (R. Vol. 49, p. 988-91.) He opined that if he had testified at the penalty phase, he would have stated that Pietri was most likely intoxicated to some degree at the time of the offense. (Id. at 993-94.) His primary diagnosis would be that the chronic effects of long term substance abuse had rendered Pietri's "capacity to conform his conduct to the requirements of the law ... significantly impaired." (Id. at 1000.)
Dr. Glen Caddy, a clinical and forensic psychologist, testified that Pietri's trial counsel hired him to examine aspects of Pietri's functioning. (R. Vol. 50, p. 1183.) Dr. Caddy conducted a background investigation of Pietri's development history and spoke to several family members. Dr. Caddy stated that he knew that trial counsel would ask him to provide information relevant to any mitigating considerations, and he would have been prepared to opine that Pietri was under extreme mental or emotional disturbance at the time of the crime. (Vol. 51, p. 1226-27.) Dr. Caddy confirmed the veracity of the testimony he had given during the penalty phase of Pietri's trial. (Id. at 1246.) Dr. Faye Sultan, a clinical psychologist, who met with Pietri several times in 2001, testified during the hearing that Pietri suffered actual brain injury as a result of childhood sexual abuse and that he had a diagnosable personality disorder. (R. Vol. 51, p. 1254-1308.)
Pietri's trial counsel also testified at the evidentiary hearing regarding the presentation of an intoxication defense. The trial counsel admitted that they considered the defense, but because there was no evidence of Pietri's actual drug intoxication at the time of the crime, they decided to rely on the lack of intent defense. (R. Vol. 47, p. 646; Vol. 48, p. 751-53, 813.) Peter Birch stated that at the time he did not think a jury would accept intoxication as a defense, even if they had the evidence to prove it, for killing a police officer. (Vol. 47, p. 645, 663.) Because there was no evidence to support the defense and counsel did not believe the intoxication defense was a strong one, they opted to proffer the lack of intent defense by arguing that Pietri was trying to secure more cocaine and acted impulsively when he shot Officer Chappell. Peter Birch testified that he spent much effort in securing a plea agreement, which they had until the night before trial. (Id. at 692.) Birch was convinced that the case was a second degree *1282 murder case because there was no premeditation. (Id. at 714-15.) He acknowledged that they presented evidence of cocaine to negate the premeditation by showing that Pietri was thinking about getting more cocaine, not about shooting the police officer. (Id. at 718-19.)
Following the evidentiary hearing, the state trial court rejected Pietri's request for post-conviction relief. Pietri appealed to the Florida Supreme Court. On appeal, the Florida Supreme Court set forth the requirements enunciated in Strickland for a petitioner to succeed on a claim of ineffective assistance of counsel. Pietri, 885 So.2d at 251-52. The appellate court then analyzed the claim under the parameters of Strickland and denied relief:
In his first claim, Pietri argues that his trial counsel were ineffective for failing to investigate and present a voluntary intoxication defense, and that if they had performed effectively, it could have been demonstrated that due to Pietri's intoxication, he lacked the requisite specific intent to commit the murder. Pietri's claim must fail, however, because Pietri did not present any evidence at the postconviction evidentiary hearing to demonstrate that he was in fact intoxicated at the time of the offense. Furthermore, he did not present any competent evidence proving his inability to form the specific intent to commit the crime. Pietri relies upon the theory that as a result of his persistent use of cocaine on the days prior to the crime he was in a state of "metabolic intoxication" at the time of the offense and, therefore, could not have formed the requisite specific intent. This Court has consistently rejected this theory, holding that evidence of "metabolic intoxication" is not admissible at trial. Because counsel cannot have been ineffective for failing to present inadmissible evidence, Pietri's first claim is denied.
Id. at 252.
The court then recognized that Pietri was not asserting that he was actually intoxicated at the time of the offense, and his own expert did not opine that Pietri was intoxicated when he shot the officer. Rather, the court noted, Pietri was asserting that his chronic drug abuse had a lasting impact, and that while he had little to no cocaine in his bloodstream at the time of the offense, he was under the effects of the cocaine to the same extent as if he was legally intoxicated. Id. at 253. The court noted that Pietri presented a total of five mental health experts at the evidentiary hearing to support his assertion:
Dr. Lipman was the only expert who explicitly expressed the opinion that Pietri lacked the specific intent to commit murder. Similar to Dr. Lipman's testimony, Dr. Krop, a clinical psychologist, testified that had he been called to offer his opinion, he would have explained that Pietri had a history of substance abuse and that he was either actively intoxicated or withdrawing from substances at the time of the offense. He would have testified concerning the effects of cocaine and how extensive use of the drug can cause individuals to have problems with judgment and impulse control, and how the drug can cause them to become paranoid and hypervigilant. Dr. Krop did not, however, offer any opinion regarding Pietri's ability to form the specific intent to commit the offense. A third expert, Dr. Caddy, testified that he could not give an exact opinion regarding what impact the cocaine had on Pietri at the time of the offense. He believes Pietri was in withdrawal and had reactive judgment problems. Dr. Caddy stated that he could *1283 not rule out the possible significance of a cocaine intoxication state which triggered Pietri into doing something he would not have otherwise done. The two remaining mental health experts offered no opinion regarding Pietri's mental state at the time of the offense, and one doctor, Dr. Goldberg, specifically noted that he never talked with Pietri about such subject. The one mental health expert presented by the State testified that based upon Pietri's ability to clearly recall the events of the crime, Pietri was able to form the specific intent to commit the offense.
While Pietri presented several witnesses at the evidentiary hearing who testified concerning his extensive drug use both historically and during the four days immediately preceding the crime, Pietri did not present any competent evidence demonstrating that he was actually intoxicated at the time of the offense. Notably, it is unlikely that there is any one who could assert that Pietri was intoxicated at the time of the offense or could even provide an opinion regarding Pietri's mental state at the time of the offense as Pietri himself testified during the guilt phase that he was alone at the time of the crime and for several hours preceding the fatal event.
Pietri has failed to demonstrate that his trial counsel provided deficient performance. The only witness presented at the evidentiary hearing who provided an opinion regarding Pietri's inability to form the specific intent required for first-degree premeditated murder was Dr. Lipman. However, even if Pietri's trial counsel had called Dr. Lipman to testify at trial, because Pietri has failed to demonstrate that he was actually intoxicated at the time of the offense, and, in fact, actually presented testimony to the contrary, it is unquestionable that the testimony of Dr. Lipman would have been inadmissible.
Although this Court has repeatedly held that evidence of voluntary intoxication is admissible to prove the defendant lacked the specific intent to commit premeditated murder, see Spencer v. State, 842 So.2d 52, 63 (Fla.2003); Chestnut v. State, 538 So.2d 820, 822 (Fla.1989), we have further held that "there are limitations regarding the admissibility of evidence of mental disease or defect within the defense of voluntary intoxication." Spencer, 842 So.2d at 63.... It is unquestionable that at the time of Pietri's trial, diminished capacity was not a cognizable defense in Florida. See Chestnut, 538 So.2d at 825. In Chestnut, we held that evidence of an abnormal mental condition not constituting legal insanity is not admissible for the purpose of proving that the defendant could not or did not entertain the specific intent necessary for proof of the offense. See id. at 820. Pietri essentially asserts that evidence could have been presented, not to show that he was legally insane or voluntarily intoxicated, but instead that his prior drug abuse resulted in a mental defect"metabolic intoxication"a diminished capacity which produced an inability to form the specific intent to commit premeditated murder. Such evidence was inadmissible.
Id., 885 So.2d at 253-55. The court concluded that because Pietri could not demonstrate that he was intoxicated at the time of the murder and the evidence of metabolic intoxication would not have been admissible at trial, Pietri's counsel were not ineffective. Id. at 255.
We conclude from the record that Pietri cannot meet his burden of showing that the state court's rejection of his claim of ineffective assistance of counsel was *1284 contrary to Strickland. The record indicates that at no time did anyone testify that Pietri did not form the specific intent to commit the murder, and Pietri did not show that he was intoxicated at the time of the murder. Pietri's trial counsel testified at his evidentiary hearing that they had considered presenting an intoxication defense, but decided against using it when they realized there was no evidence showing that Pietri was intoxicated at the time of the offense. (R. Vol. 47, p. 646; Vol. 48, p. 751-53, 813.) Thus, the state appellate court's finding that trial counsel were not ineffective because they did not proffer a defense they could not support, was neither contrary to, nor an unreasonable application of, Strickland. Pietri is not entitled to relief on this claim. See Powell v. Allen, 602 F.3d 1263, 1275 (11th Cir.2010) (rejecting claim of ineffectiveness for not raising an intoxication defense where defendant failed to come forward with supporting evidence on collateral review), cert. denied, ___ U.S. ___, 131 S.Ct. 1002, 178 L.Ed.2d 834 (2011). Furthermore, both counsel testified that even if the evidence supported an intoxication defense, they would not have proffered it because, based on their experience, it was not successful among jurors.
The state appellate court also found that Pietri's "metabolic intoxication" defense was not cognizable under Florida law at the time of Pietri's trial. A state supreme court's interpretation of its law is binding on federal courts. See Mullaney v. Wilbur, 421 U.S. 684, 690-91, 95 S.Ct. 1881, 1885-86, 44 L.Ed.2d 508 (1975). Because this defense was not viable under state law at the time of Pietri's trial, his counsel cannot be deemed ineffective for failing to proffer it. See Michael v. Crosby, 430 F.3d 1310, 1321-22 (11th Cir.2005) (holding that counsel was not ineffective for failing to pursue a theory of defense that was not cognizable under Florida law).
Even if Pietri could show that his counsel were ineffective for failing to proffer a voluntary intoxication defense, Pietri could not demonstrate that their deficient performance prejudiced him. We have commented that detailed evidence of extensive drug abuse can be "a two-edged sword." Housel v. Head, 238 F.3d 1289, 1296 (11th Cir.2001) (citation omitted). This evidence may have had a counter-productive effect on the jury, and counsel testified at the post-conviction evidentiary hearing that it was generally not a successful defense. Pietri cannot satisfy the two requirements set forth in Strickland, and, therefore, he is not entitled to relief on this claim of ineffective assistance of counsel.

B. Ineffective Assistance of Counsel at the Penalty Stage

Pietri claims that his counsel were ineffective at the penalty phase for failing to investigate and present mitigating evidence of his low IQ, brain damage, childhood sexual and physical abuse, and cocaine addiction. Pietri asserts that because his counsels' deficient performance prejudiced his sentence, the state court's disposition of this claim was an unreasonable application of Strickland and Wiggins.
In reviewing this claim, we consider the testimony of the eight witnesses that defense counsel did present during the penalty phase of Pietri's trial. Pietri's older brother, William Pietri, testified that their father was a violent man, an alcoholic who beat their mother and abandoned the family when petitioner was very young. (R. Vol. 19, p. 2826-37; Vol. I. Penalty phase, p. 38-48.) William stated that Pietri was a "very nice kid" before he became involved with drugs. (Id. at 2834; Vol. I at 45.) Another brother, Marino Pietri, testified that his parents had nine children from *1285 their union, and the entire family lived together in one house that had only two bedrooms, a living room, and a kitchen. (Id. at 2849-87; Vol. I at 60-98.) The house did not have running water, an indoor bathroom, or television. Marino corroborated William's testimony about their father's alcoholism, physical and psychological abuse to family members, and abandonment. Marino explained that Pietri had a cross-eye condition and had surgery to correct the problem, but the surgery caused him to be blind in his right eye. Marino stated that Pietri worked with him for several years in the landscape business, but then Pietri started using drugs and was no longer a good worker.
Defense counsel also presented Pietri's sisters, Ramona Rivera and Ada Serrano Liddell, as witnesses. (Id. at 2888-96; Vol. I at 99-107 and Id. at 2901-11; Vol. II Penalty phase, p. 112-22.) Both testified that Pietri was a fun person and a nice brother, who changed substantially after he began using cocaine. Roger Paul, a minister who met with Pietri while he was incarcerated, testified that Pietri had undergone a religious transformation which led him to admit to his crime and express remorse for his crime. (Id. at 2912-25; Vol. II at 123-36.) The defense also presented Yoris Santana, who was with Pietri during the days immediately prior to the murder, after Pietri escaped from prison. (Id. at 2838-46; Vol. I, 49-57.) Santana explained that during the days preceding the murder, Pietri was involved in heavy drug use, specifically "rock cocaine." Santana testified that Pietri used cocaine "24/7" and had problems when he was high on drugs. (Id. at 2839; Vol. I at 50.)
Defense counsel also presented the testimony of two experts at the penalty phase. Jody Iodice, a social worker and former drug addict who worked extensively with drug addicts, explained the effects of cocaine, the type of people more likely to become addicted to drugs, the "crash" that occurs following the use of drugs, the length of the crash symptoms, the "down phase" after cocaine use, and the length of the "down phase." (Id. at 2925-52; Vol. II, p. 136-63.) However, she also explained that drug use does not impair intellect and does not impair the ability to make cognitive decisions. (Id. at 2944; Vol. II at 155.) Ms. Iodice also stated that the drug use may alter a person's priorities, but the person can still distinguish between right and wrong. (Id. at 2945; Vol. II at 156.) Defense counsel did elicit from Ms. Iodice the fact that people on drugs do not anticipate the consequences of their actions, and their actions are produced by pure impulse. She also acknowledged that cocaine does alter one's judgment, and that for people on drugs, everything is based on their drive to obtain the drug. (Id.)
The defense also presented the testimony of Dr. Glen Caddy, a mental health expert, who explained that he had consulted with Pietri prior to his testimony, had conducted a mental status exam, and had obtained a personal history on Pietri. (Id. at 2952-3024; Vol. II p. 163-236.) Dr. Caddy opined that Pietri had a very chaotic and tragic childhood, and his family life lacked structure and limitations. Dr. Caddy's examination of Pietri's history revealed that he had an eye condition that resulted in the loss of sight in his right eye; his father was often drunk and very abusive; his father beat his mother almost daily in the presence of the children; his father also exhibited violence toward the children; he was sexually abused for about two years by a man who lived with the family; and his mother was totally ineffective as a parent. Dr. Caddy testified that around the age of 13, Pietri began engaging in aberrant behavior, and by the age of 14, he had already become very vulnerable to drug use, abuse, and addiction. Dr. *1286 Caddy noted that Pietri dropped out of school when he was sixteen, used drugs and drank excessively, then pulled himself together for a brief period before he entered the world of cocaine. Pietri began to commit crimes to support his drug habit. Dr. Caddy explained that Pietri's incarceration period was just a "time-out" from drug addiction. (Id. at 2984; Vol. II at 196.)
Dr. Caddy explained the effects of drug addiction and noted that during the withdrawal period, a drug addict overreacts to stimuli. The addict may experience a general sense of confusion and a high stress level. Dr. Caddy opined that on the day of the offense, Pietri was still experiencing the residual effects of having ingested cocaine for the prior three or four days. (Id. at 2989-90; Vol. II at 201-02.) He explained that Pietri's main focus around the time of the murder was to acquire more cocaine, and his judgment would have been impaired. Dr. Caddy also recounted the events Pietri had related to him concerning the offensethat Pietri had become frightened when he was aware that a police officer was following him, and as he stuffed stolen jewelry into his pocket, he felt the gun, picked it up and fired at the officer. Dr. Caddy opined that Pietri's conduct was simply a reaction, which is consistent with someone who uses cocaine heavily. (Id. at 2994-95; Vol. II at 206-07.)
Despite the defense testimony presented during the sentencing phase of his trial, Pietri claims that his counsel could have and should have done more to investigate and present mitigation evidence. At his evidentiary hearing, Pietri presented expert and counsel testimony to elaborate on the mitigation evidence that he alleges counsel failed to present at the sentencing phase.
Dr. Jonathan Lipman testified that had he been called during the penalty phase, he would have opined that Pietri was under the influence of an extreme mental or emotional disturbance at the time of the crime. In his opinion, Pietri could appreciate the criminality of his conduct, but his ability to conform his behavior to the requirements of the law was impaired. (R. Vol. 50, p. 1104.) Dr. Lipman concluded, based upon his evaluation of Pietri and Pietri's extensive drug use, that Pietri did have an organic mental disorder caused by his toxic condition at the time of the offense. (Id. at 1151.) Dr. Glen Caddy stated that the opinions and conclusions he proffered at the penalty phase had not changed. (R. Vol. 51, p. 1246.) He acknowledged that he could not testify that Pietri's mental state at the time of the crime was extremely impaired nor could he testify that Pietri was unable to appreciate the criminality of his conduct. (Id. at 1226-28.) Dr. Harry Krop testified and conceded that much of the information he provided during the evidentiary hearing was the same as that covered by Dr. Glen Caddy during his penalty phase testimony. (R. Vol. 49, p. 970-1031.)
Dr. Faye Sultan also testified and described, in detail, Pietri's recollections of being sexually abused as a child. (R. Vol. 51, p. 1254-1308.) Dr. Sultan opined that a person who has been sexually abused is more likely to become an early abuser of drugs and alcohol. She also opined that a sexual abuse victim would have difficulty regulating his emotions and would be more likely to experience the severe effects of any chemical he used. Dr. Sultan conceded that Dr. Caddy's findings were consistent with her opinion. The last mental health expert to testify was Dr. Goldberg, who conducted a battery of psychological tests on Pietri and concluded that Pietri's IQ is 76, which places him in the mildly impaired range. (R. Vol. 53, p. 1495-1705.) He opined that Pietri's cognitive impairments are due to cerebral dysfunction. *1287 When asked if Pietri satisfied any of the mental health mitigating factors listed in the statute, he responded that Pietri satisfied only the "catchall criteria." See Fla. Stat. § 921.141(6)(h) (2010). (Id. at 1522.)
Peter Birch, Pietri's penalty-phase counsel, testified at the evidentiary hearing that he focused more time on the guilt phase of Pietri's trial in an attempt to secure an advantageous plea agreement. One week before trial began, Birch believed that the trial would not start because there was a written, signed plea agreement between Pietri and the State. (R. Vol. 47 p. 692.) Birch also stated that he attempted to secure a mental health expert for the penalty phase and finally had Dr. Krop appointed about one month before the scheduled trial. After Dr. Krop evaluated Pietri, he advised Birch that in his opinion, Pietri was competent to proceed and was sane at the time of the offense. (Id. at 624-29.) Dr. Krop also advised Birch that Pietri had no psychiatric history or evidence of any psychotic process disturbance or organic disorder. Dr. Krop did report that Pietri had a history of substance abuse and possible physical and sexual abuse. Birch stated that he was disappointed in Dr. Krop's opinion and decided that he would not use Krop as an expert at the penalty phase because he would have been of little assistance. (Id. at 629.)
After unsuccessfully soliciting the assistance of Dr. Krop, Birch testified that he contacted another mental health professional, Dr. Haynes. Birch consulted with Dr. Haynes several times, then he and his co-counsel Donnie Murrell decided that Dr. Haynes would not be helpful. (Id. at 669-70.) Birch recalled talking to other mental health experts after Dr. Haynes, and five days before the penalty phase began, secured the assistance of Dr. Caddy. Birch acknowledged that the defense had a lot of evidence to support non-statutory mitigation. (Id. at 676.)
The state appellate court rejected Pietri's contentions that his penalty-phase counsel were ineffective. Based on Peter Birch's testimony, the Florida Supreme Court concluded that Pietri failed to demonstrate that his counsel were deficient in securing a mental health expert.
Although counsel was admittedly not focused on the penalty phase from the outset or in the months prior to the start of the guilt phase trial, the record clearly reflects that counsel began attempts to secure a mental health expert well before the penalty phase began. There was evidence of clear justification for not utilizing Dr. Krop as a witness, ... and counsel subsequently contacted at least four experts before finally locating one who could offer assistance .... While there is no claim here that Pietri was uncooperative, the record does reflect that at least one of the mental health experts contacted by defense counsel, Dr. Haynes, was unwilling to testify. Here we do not even have deficient results because the evidence ultimately presented at trial encompassed the material for which Pietri now asserts fault with counsel.
Pietri, 885 So.2d at 263-64. The court then concluded that even if counsel were deficient in their attempts to secure a mental health expert, it was clear that Pietri failed to demonstrate that he suffered prejudice as a result of the alleged ineffectiveness. The Florida Supreme Court noted that none of the experts who testified at the evidentiary hearing claimed any inadequacies in either Dr. Caddy or Jody Iodice's penalty-phase testimony. Id. at 266. In fact, Dr. Krop and Dr. Sultan acknowledged that their testimony was consistent with Dr. Caddy's penalty-stage testimony. Because the jury was *1288 presented with identical evidence of the effects of Pietri's drug usage at the penalty stage, the appellate court concluded that there was no probability that the additional evidence presented at the evidentiary hearing would have changed the outcome of the sentence. Id.
We agree with the Florida Supreme Court that Pietri cannot show that his penalty-phase counsel were unconstitutionally ineffective. Pietri cannot demonstrate that the state court unreasonably applied Strickland to the facts of his case. The state court reviewed the testimony presented at both the penalty phase and the post-conviction hearing. It noted that trial counsel made numerous attempts to secure a mental health expert and strategically decided not to present some of the mental health experts they consulted. Additionally, the state appellate court found that the penalty-phase jury was presented with identical evidence of the effects of long-term or continuous drug use that Pietri presented at the collateral hearing. Thus, the state appellate court determined that counsel did not provide constitutionally deficient performance, but even if they did, there was no reasonable likelihood that the result of Pietri's sentencing would have been different based on this additional information. Pietri has not satisfied his burden of showing that the state court applied Strickland to his case in an objectively unreasonable manner. See Woodford, 537 U.S. at 25, 123 S.Ct. at 360. Accordingly, we affirm the district court's order denying Pietri relief on this claim of ineffective assistance of counsel.

C. Ineffective Assistance of Appellate Counsel

Pietri contends that the district court erred in finding unexhausted his claim that appellate counsel failed to object to the trial court's judicial bias. Pietri asserts that he preserved the issue in state court and that the district court therefore erred in dismissing the claim.
In his amended post-conviction petition pursuant to Florida Rules of Criminal Procedure Rule 3.850, Pietri argued that his Eighth Amendment right was violated by the sentencing court's refusal to find and/or consider the mitigating circumstances set out clearly in the record. Elaborating on this argument, Pietri stated that he presented evidence of mitigation, such as his extreme poverty during childhood, the physical and sexual abuse he endured as a young person, and his drug and alcohol addiction. He concluded by positing that his death sentence was arbitrary and capricious because the sentencing court did not properly weigh the aggravating and mitigating circumstances. In this same petition, Pietri also argued that he was denied his right to a fair trial and sentencing before an impartial judge in violation of his Fifth, Sixth, Eighth, and Fourteenth Amendment rights because the sentencing court was biased in favor of the State. (Id. Claim XXXII, p. 109.) Pietri stated that examples of the sentencing court's bias included its failure to grant Pietri's motion for change of venue, its allowance of challenges for cause by the State, its failure to grant Pietri a continuance of the sentencing phase, and its failure to find any mitigation at sentencing. The trial court denied both of these claims on procedural grounds.
On appeal from the trial court's order denying him post-conviction relief, Pietri argued that counsel was ineffective for failing to challenge the trial court's finding regarding mitigation. He claimed that the trial court adopted the State's findings in its post-evidentiary memorandum and incorporated them into its sentencing order, thus denying him a full and fair tribunal under state law. Along with his appeal from the trial court's denial of his post-conviction *1289 motion, Pietri filed a state habeas petition in which he claimed that appellate counsel was ineffective for failing to challenge the trial court's adverse ruling on the motion for change of venue. On appeal, the Supreme Court of Florida denied Pietri post-conviction and habeas relief. Pietri, 885 So.2d at 276. The state appellate court found no merit to Pietri's claim that the trial court erred in incorporating the State's post-evidentiary hearing memorandum. Id. at 270. The appellate court found procedurally barred Pietri's state habeas claim that appellate counsel was ineffective for failing to challenge the trial court's ruling denying Pietri's motion for a change of venue. Id. at 273.
On appeal, Pietri contends that the district court erred in dismissing his claim that appellate counsel failed to challenge the trial court's impartiality because he exhausted the substantive claim of judicial bias. However, contrary to Pietri's contention, he did not preserve the substantive judicial bias claim because he did not present the claim to the Supreme Court of Florida. See O'Sullivan v. Boerckel, 526 U.S. 838, 842-45, 119 S.Ct. 1728, 1731-33, 144 L.Ed.2d 1 (1999) (holding that in order for a claim to be exhausted, the petitioner must invoke one complete round of the State's established appellate review process). Furthermore, Pietri's assertion of a substantive judicial bias claim in state post-conviction proceedings is not sufficient to preserve his claim of ineffective assistance of appellate counsel for failing to raise the substantive claim. These claims are separate and distinct. See LeCroy v. Sec'y for Fla. Dep't of Corrs., 421 F.3d 1237, 1260 n. 24 (11th Cir.2005) (noting that substantive claim was "separate and distinct" from ineffective assistance claim based on the substantive claim). Because he never raised this specific claim of ineffectiveness, the district court properly dismissed it. See 28 U.S.C. § 2254(b)(1); Kelley v. Sec'y for Dep't of Corrs., 377 F.3d 1317, 1343-44 (11th Cir.2004) (noting that petitioners may not present particular factual instances of ineffective assistance of counsel in their federal petition if they did not first raise them in the state courts). Accordingly, the district court properly dismissed as unexhausted the ineffectiveness of appellate counsel claim.

V. CONCLUSION
The district court did not err in denying Pietri habeas relief. Accordingly, we affirm the district court's judgment.
AFFIRMED.
NOTES
[1]  This is an individual who studies the properties and reactions of a drug on and in the nervous system.
