ED CARNES, Chief Judge:

This is an appeal and cross-appeal from a judgment granting in part and denying in part the federal habeas petition of Florida death row inmate Richard Lynch. See 28 U.S.C. § 2254. He was sentenced to death in 2001 for the 1999 murder of thirty-year-old Roseanna Morgan and her thirteen-year-old daughter, Leah Caday. The State of Florida's appeal is from the part of the judgment granting Lynch habeas relief based on his claim that he was denied the effective assistance of counsel because his attorneys advised him, after he had entered a guilty plea, to waive his right to a jury in the sentence stage of his capital trial. Lynch cross-appeals the part of the judgment denying three of his other ineffective assistance claims that he raised in his habeas petition.

I.

Lynch murdered Morgan and Caday on March 5, 1999, because he could not accept Morgan's decision to end their extramarital affair. See Lynch v. State, 841 So.2d 362, 366 (Fla.2003). The affair had lasted from August 1998 until February 1999. Id. While it was underway, although Lynch was unemployed and relied on his wife for financial support, he obtained three credit cards that were used to make more than $6,000 worth of purchases for Morgan. See Lynch v. State, 2 So.3d 47, 66 (Fla.2008). She ended the affair on February 9, 1999 after her husband returned from Saudi Arabia where he had been working as a military contractor. See Lynch, 841 So.2d at 374. While Morgan moved on, Lynch did not. He began stalking Morgan, hanging around her apartment complex, showing up at her job, following her on her way home from work, and calling her apartment. Morgan's husband confronted Lynch several times and told him to leave her alone, but it did no good. Lynch persisted.

On March 3, 1999, about three weeks after Morgan had ended the affair, Lynch wrote a letter to his wife declaring his intention to kill Morgan and then himself. See id. at 366, 368. In that letter he asked his wife to send Morgan's parents copies of the letters and cards Morgan had written to him, as well as nude pictures of Morgan that he had taken. Id. at 366. He wrote that "I want them to have a sense of why it happened, some decent closure, a reason and understanding.... I want them to know what she did, the pain she caused, that it was not just a random act of violence." Lynch, 2 So.3d at 64 (emphasis omitted). Lynch went on in the letter about the debts that had been run up on the credit cards, his fear that Morgan would not pay him back for any of the purchases, and the pain that she had caused him by ending their affair. After describing in explicit and unnecessary detail the various sexual acts he and Morgan had engaged in and how much he had enjoyed them, on the last page of the letter Lynch apologized to his wife "for all the pain, suffering, expense, embarrassment and hardship I will cause and give to you," but concluded that Morgan "must pay the price." Lynch left the letter in his garage.

Two days later, on March 5, he packed three pistols and ammunition into a black bag and drove to Morgan's apartment. See id. at 59. He parked his car down the street and around the corner from the apartment complex so that Morgan and her daughter Caday would not see it when they arrived at the complex. Id.; Lynch, 841 So.2d at 367 n. 3. Lynch grabbed the bag with the three pistols and ammunition from the trunk of his car, walked to the complex, and picked an inconspicuous spot to wait for Morgan to return. See Lynch, 2 So.3d at 76.

Caday got home first. See id. Lynch talked the thirteen-year-old into letting him inside by telling her that he wanted to speak with her mother. See id. at 62. Once inside the apartment, he pulled one of the pistols from the black bag and held Caday at gunpoint for thirty or forty minutes while waiting for Morgan to arrive. See Lynch, 841 So.2d at 366. All the while, the young girl was "terrified." Id. She asked Lynch "why he was doing this to her." Id.

When Morgan finally returned home, Lynch met her at the door with a pistol in his hand. See Lynch, 2 So.3d at 59. Sensing what Lynch was going to do, Morgan refused to come inside. They had a heated discussion, which ended when Lynch fired seven shots. See id. at 58, 70. Three of the shots hit Morgan in the legs. See id. at 53, 69-70. One hit her eye and tore through her neck. See id. at 69-70. She fell to the floor in the hallway outside her apartment, bleeding and screaming for help. See Lynch, 841 So.2d at 366, 371. Lynch walked outside the apartment into the hallway where Morgan lay, and the door closed behind him. He dragged Morgan's bleeding body by her wrist back to the door, where he knocked and told Morgan's daughter to "Hurry up, open the door, your mom is hurt." Id. at 367. When Caday opened the door, Lynch dragged her mother inside, closing the door behind him. Id.

Inside the apartment, Lynch pulled a second pistol from his bag, and several minutes after he had first shot Morgan he killed her in front of her daughter by firing a single, execution-style shot to her head. See id. at 370-73; Lynch, 2 So.3d at 69. He then called his wife at their home, Lynch, 841 So.2d at 366, and told her he was "sorry for what I'm going to do." During that phone call, Lynch's wife could hear Caday screaming hysterically in the background. See id. at 369. After Lynch hung up, he killed the young girl by shooting her in the back. See id. at 366.

Lynch then called his wife again. Id. He told her that he had accidentally shot Caday and told her that he had left a letter in the garage. See id. When that call ended, Mrs. Lynch dialed 911. She told the operator about Lynch's phone calls and asked for the police to investigate. She then began to look for the letter. Her sister Juliette, whom Mrs. Lynch had paged after Lynch's first phone call, arrived at the home and joined in the search. Mrs. Lynch found the letter and started to read it but was interrupted when her husband called a third time. Both she and Juliette talked to him, begging him not to kill himself. See id. While Juliette was speaking with Lynch, Mrs. Lynch used her cell phone to call 911 again. She told the operator about the murder-suicide letter she had just found and that Lynch was willing to turn himself in. After that 911 call ended and Lynch had ended his call to Mrs. Lynch, she returned to reading the letter he had left. Before she could finish reading it, several police officers arrived at her home. See Lynch, 2 So.3d at 68. One officer, after confirming that she was Mrs. Lynch, asked her for the letter. See id. She did not want to hand it over until she had finished reading it, but the officer kept asking and she gave him the letter.

While Mrs. Lynch was talking with the officers, Lynch himself called 911. See Lynch, 841 So.2d at 370. He talked with the 911 operator for the next thirty or forty minutes. See Lynch, 2 So.3d at 57-58. By the time that call began, two officers were at Morgan's apartment responding to the neighbors' reports of shots fired. The officers attempted to enter the apartment, but quickly retreated when Lynch fired a shot at them. See Lynch, 841 So.2d at 366. Eventually, the SWAT team arrived, there were negotiations, and Lynch gave himself up. Before he did that, Lynch told the 911 operator that he had killed two people, that he had shot Morgan to "put her out of her misery," and that he had fired at the two police officers who tried to enter the apartment. Id.

II.

A Florida grand jury issued a four-count indictment on March 23, 1999, charging Lynch with: (1) first-degree premeditated murder of Roseanna Morgan; (2) first-degree premeditated murder of Leah Caday; (3) armed burglary of a dwelling; and (4) kidnapping. See id. at 365-66. There was a mountain of evidence against Lynch, piled up stone by stone through the testimony of multiple witnesses, the presentation of documents, undisputed circumstances, and Lynch's own words. It was conclusively proven that: Lynch had barricaded himself inside Morgan's apartment, had fired from it at police officers, and when he emerged had left inside two dead bodies, one of which was riddled with five bullets. The prosecution also presented: the murder-suicide letter Lynch had written two days before the murders, the testimony of the neighbor across the hall who saw Lynch drag Morgan inside the apartment after she had been shot several times, the testimony of a second neighbor who described the five to seven minute pause between the two groups of gunshots, the testimony of Mrs. Lynch about his three phone calls to her, the recording of his own lengthy 911 call, the testimony of the police negotiator who talked Lynch out of the apartment, and a videotape of Lynch's post-arrest interview confessing to the killings. See Lynch, 841 So.2d at 366-67, 371.

Together, the evidence showed that: (1) two days before the murder Lynch wrote about his intent to kill Morgan; (2) he packed a bag with three loaded pistols and took them to her apartment; (3) he intentionally parked away from the apartment complex so that neither victim would see his vehicle and know he was there; (4) he held the thirteen-year-old Caday in the apartment at gunpoint for thirty or forty minutes while waiting for Morgan to return home; (5) he shot at Morgan a total of eight times, hitting her five times; (6) Morgan was still breathing when he switched to a different pistol and fired the final shot into the back of her head; (7) he said that he had fired that last shot to "put her out of her misery," but he had not done it until five to seven minutes after the first of the five shots he had fired into her; and (8) Caday watched her mother suffer from the other gunshot wounds for those five to seven minutes before he killed both of them. Lynch, 2 So.3d at 53, 59, 66, 69-70; Lynch, 841 So.2d at 366, 368-69. The only evidence in Lynch's favor, if it can be called that, was a few self-serving statements — sprinkled among his numerous incriminating admissions — in which he claimed that the initial shots he fired at Morgan through the doorway and the single shot fired into Caday had been accidental. See, e.g., Lynch, 2 So.3d at 66. He never explained how the first pistol had accidentally discharged, not once, not twice, not three or four times, but seven times. See id. at 68-70; Lynch, 841 So.2d at 378.

Lynch's two trial attorneys, who had more than twenty-five years of capital case experience between them, understandably concluded that it would be impossible to persuade a jury that Lynch had accidentally killed Morgan. See Lynch, 2 So.3d at 57-58. They believed from their experience that juries tended to be quite unsympathetic in the sentence stage to defendants who had murdered children. See id. at 57, 71. They also knew that the trial judge — Judge O.H. Eaton, Jr. — was a seasoned jurist and a recognized authority on Florida's death penalty procedure, which they believed would make him more receptive to their mitigation arguments. See id. at 72, 82. For those reasons Lynch's two experienced trial counsel advised him to plead guilty to all four counts and waive his right to a sentence-stage jury. He did so in October 2000. See id. at 52, 70-71; Lynch, 841 So.2d at 366.

III.

At the sentence hearing, which was held in January 2001, the defense built its mitigation case on the testimony of forensic neuropsychologist Dr. Jacquelyn Olander. See Lynch, 841 So.2d at 367; Lynch, 2 So.3d at 72. She testified that Lynch had a schizoaffective disorder, which was a combination of schizophrenia and a mood disorder. See Lynch, 841 So.2d at 367. She concluded that he was "under the influence of an extreme mental and emotional disturbance" when he committed the murders "and that his psychotic process substantially impaired his capacity to conform his conduct with the requirements of the law." Id.

The State called its own expert, psychologist Dr. William Riebsame. See id. at 374. He agreed with Dr. Olander that Lynch had mental health issues but disagreed about their severity. See id. In Dr. Riebsame's opinion, Lynch's lack of delusions and his ability to recall the facts of the crime were inconsistent with a schizoaffective disorder. Id. He concluded that while Lynch was "emotionally disturbed" he had not been acting under a severe mental or emotional disturbance during the crimes, and his ability to conform his conduct to the requirements of the law "was impaired, but not substantially impaired." Id.

The trial court considered all of the expert testimony, along with the evidence establishing Lynch's conduct before, during, and after the murders. See id. at 368. After having the matter under submission for two months, the court issued a written order sentencing Lynch to death for each murder. The order specified three statutory aggravating factors that supported imposing the death penalty for each of the two murders. See id.

The trial court rested the death sentence for Morgan's murder in large part on the fact that Lynch had planned days in advance to kill Morgan and then had methodically carried out his plan. It placed "great weight" on the statutory aggravating circumstance that "the murder was cold, calculated, and premeditated." Id. (applying Fla. Stat. § 921.141(5)(i)). The court put "moderate weight" on the aggravating circumstance that Lynch "had previously been convicted of a violent felony." Id. (applying Fla. Stat. § 921.141(5)(b)). It reasoned that the previously-convicted-of-a-violent-felony factor applied because the murder involved multiple victims1 but decided that factor should receive only moderate weight because Morgan was the first victim killed. The court also found the aggravating circumstance that Lynch had committed the murder "while ... engaged in committing one or more other felonies." Id. (applying Fla. Stat. § 921.141(5)(d)). It reasoned that the circumstance applied because Lynch had killed Morgan in the course of committing armed burglary,2 but it concluded that the factor should be given little weight since the armed burglary was part of Lynch's premeditated plan and thus already covered by the "cold, calculated, and premeditated" aggravating circumstance.

On the other side of the scale, the trial court found that the only statutory mitigating factor that applied was the one for "no significant history of prior criminal activity," and that it should receive only "moderate weight." Id. at 368 & n. 5. Lynch contended that two more statutory mitigating factors should apply — that he had committed the murders while "under the influence of extreme mental or emotional disturbance" and that his capacity "to conform his ... conduct to the requirements of law was substantially impaired." See Fla. Stat. § 921.141(6)(b), (f). The court determined, however, that the circumstances on which Lynch based those contentions were entitled to only "moderate weight" as non-statutory mitigating circumstances because Lynch had not proven that his disturbance or impairment was great enough to meet the statutory mitigating circumstances definitions. See Lynch, 841 So.2d at 374-75. The court also found six other non-statutory mitigating circumstances for a total of eight.3

Concluding that the three aggravating factors outweighed the one statutory mitigating factor and the eight non-statutory mitigating factors, the court sentenced Lynch to death for the murder of Morgan. See id. at 368 & n. 5.

For Caday's murder, the trial court's determination that a death sentence was warranted centered on the terror that Caday had experienced before she died. The court placed "great weight" on the fact "that the murder was heinous, atrocious, or cruel." Id. at 368 (applying Fla. Stat. § 921.141(5)(h)). It reasoned that the fear and emotional strain Caday had suffered from the time Lynch talked her into letting him into the apartment until he shot her to death made her murder heinous. It noted that Lynch had held the terrified young girl at gunpoint for thirty or forty minutes before her mother arrived and then shot her mother dead in front of her. Caday was screaming hysterically during Lynch's first phone call to his wife.

The court found that Lynch had been "previously convicted of a violent felony," id. (applying Fla. Stat. § 921.141(5)(b)), and it placed "great weight" on that aggravating circumstance because Caday was the second victim killed in a multiple murder. The court also found the aggravating circumstance that Lynch had killed Caday while he "was engaged in committing one or more other felonies," id. (applying Fla. Stat. § 921.141(5)(d)), because Caday was a minor.4 But it decided that the factor should receive only moderate weight because Caday's "killing was an after-thought" and would have been second-degree murder but for the felony murder rule.

The court found the same statutory and non-statutory mitigating circumstances it had in sentencing Lynch for the murder of Morgan, and concluded that the three aggravating circumstances outweighed that single statutory mitigating factor and the same eight non-statutory mitigating factors, justifying a sentence of death for Caday's murder. See id. at 368 & n. 5.

IV.

On direct appeal, the Florida Supreme Court rejected all of Lynch's many challenges to his convictions and sentences. See id. at 379. That happened in 2003. Lynch then filed a motion for post-conviction relief raising a new set of issues. See Lynch, 2 So.3d at 54-55. Many of those issues turned on the fact that his trial counsel had not obtained expert testimony showing that Lynch had a brain impairment. See id. at 54. The evidence that Lynch presented at the state post-conviction hearing included testimony: from his trial counsel explaining their representation of Lynch, from the two mental health experts who examined Lynch before the sentence hearing, and from three new mental health experts who had examined Lynch since the trial for signs of brain damage. See id. at 74-75. The state post-conviction court denied Lynch's petition in October 2006, and the Florida Supreme Court affirmed that denial in November 2008. See id. at 55-56, 86.

In April 2009 Lynch filed a petition for a writ of habeas corpus under 28 U.S.C. § 2254. In September 2012 the district court issued an order granting the petition as to the death sentence based on the claim that Lynch had been denied effective assistance of counsel when his attorneys advised him to waive a sentence-stage jury. Lynch v. Sec'y, Dep't of Corr., 897 F.Supp.2d 1277, 1306-09, 1351 (M.D.Fla. 2012). The State appealed the grant, while Lynch sought a certificate of appealability for a cross-appeal of the denial of four additional claims. We granted him a certificate on three ineffective assistance of counsel claims involving his assertions that defense counsel had: (1) unreasonably advised Lynch to plead guilty to all four counts in the indictment; (2) failed to file a Fourth Amendment suppression motion to exclude his murder-suicide letter at the sentence stage; and (3) failed to conduct a reasonable mitigation investigation and present available mitigating circumstance evidence at the sentence stage.

V.

"When reviewing a district court's grant or denial of habeas relief, we review questions of law and mixed questions of law and fact de novo, and findings of fact for clear error." Reaves v. Sec'y, Fla. Dep't of Corr., 717 F.3d 886, 899 (11th Cir.2013) (quotation marks omitted).

The Florida Supreme Court denied on the merits all four of the claims that we are considering, so we review its decision under the standards set by AEDPA. See Holsey v. Warden, Ga. Diagnostic Prison, 694 F.3d 1230, 1257 (11th Cir.2012). Those standards preclude federal habeas relief 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). That leaves Lynch with a difficult task. He must show that "no `fairminded jurist' could agree" with the state court's decision on an issue of federal law or on an issue of fact. Holsey, 694 F.3d at 1257 (citing Harrington v. Richter, 562 U.S. 86, 131 S.Ct. 770, 786, 178 L.Ed.2d 624 (2011)).

Because the three issues raised in Lynch's cross-appeal precede — either chronologically or logically — the issue raised in the State's direct appeal, we address those three claims first. After that we will address the State's challenge to the part of the district court's judgment granting Lynch relief.

VI.

Lynch's cross-appeal raises three ineffective assistance claims. The first claim faults defense counsel for advising him to plead guilty. The second criticizes defense counsel for failing to file a Fourth Amendment suppression motion to exclude his murder-suicide letter. And the third claim castigates defense counsel for not procuring and presenting at the sentence stage expert testimony that Lynch suffers from a brain impairment.

A. Advice to Plead Guilty

Lynch contends that he received ineffective assistance of counsel when his trial attorneys advised him to plead guilty to all four counts in the indictment. He argues that the advice to plead guilty was deficient because he had potential defenses to the charges of first-degree murder, burglary, and kidnapping. To succeed on this claim, Lynch must prove that: (1) counsel's advice was deficient; and (2) "but for counsel's errors, he would not have pleaded guilty and would have insisted on going to trial." Hill v. Lockhart, 474 U.S. 52, 58-59, 106 S.Ct. 366, 370, 88 L.Ed.2d 203 (1985).

The Florida Supreme Court held that Lynch failed to satisfy either prong of Hill. It concluded that counsel's advice to plead guilty and "concentrate on presenting compelling mitigation evidence" was a "reasonable strategic determination" given the "overwhelming evidence" of Lynch's guilt on all four charges. Lynch, 2 So.3d at 57. The court then addressed the prejudice question. The defenses that Lynch claimed his counsel failed to inform him about were not affirmative defenses but instead were all based on the absence of an element of the crime. He faulted counsel for not telling him that: (1) lack of intent was a defense to first-degree murder, (2) entry with consent was a defense to burglary, and (3) kidnapping requires the confinement of the victim to be both significant and not incidental to another crime. See id. at 57-62. The Florida Supreme Court concluded that Lynch was not prejudiced by counsel's alleged failings because the evidence clearly established all of the elements of all three offenses. See id. at 59-63.

The district court held that the Florida Supreme Court's application of Hill was reasonable, in part, because Lynch had not established prejudice. Lynch, 897 F.Supp.2d at 1328-33. We agree.5 The evidence of Lynch's guilt, which we have already recounted, was overwhelming. See supra Part II. And the Florida Supreme Court's thorough assessment of the evidence and the facts it established convinces us that Lynch had no viable innocence defense at trial. See Lynch, 2 So.3d at 59-63. He was not prejudiced by his attorneys' alleged failure to inform him of possible defenses, and his claim to the contrary completely lacks merit.

Lynch does not challenge the Florida Supreme Court's explanation about why he had no viable defenses to the charges. Instead, he asserts that the court unreasonably applied Hill by focusing on whether Lynch's defenses likely would have prevailed at trial. That is, however, what Hill instructs courts to do in determining whether the defendant would have insisted on going to trial. See 474 U.S. at 59, 106 S.Ct. at 371 ("[W]here the alleged error of counsel is a failure to advise the defendant of a potential affirmative defense to the crime charged, the resolution of the `prejudice' inquiry will depend largely on whether the affirmative defense likely would have succeeded at trial.").6 The Florida Supreme Court did not unreasonably apply Hill.7

Lynch also claims that counsel were ineffective for advising him to enter "a blind guilty plea," which is one entered without any benefit in return from the prosecution. In support of this claim, he cites our decision in Esslinger v. Davis, 44 F.3d 1515 (11th Cir.1995). But Esslinger expressly disclaims the broad proposition for which Lynch cites it. See id. at 1530 ("We do not hold that an attorney who recommends a blind plea inherently fails to perform as required by the Sixth Amendment.") (emphasis added). In that case, counsel had failed to adequately research the defendant's prior criminal history before advising him to plead guilty to first-degree rape. See id. at 1529-30. As a result, the defendant pleaded guilty because he believed that he would get a ten-year sentence, only to discover at the sentence hearing that his prior convictions triggered a statutorily mandated minimum sentence of ninety-nine years. Id. at 1517-18. We held that Esslinger was denied the effective assistance of counsel because the evidence established a reasonable probability that he would not have pleaded guilty to first-degree rape if his counsel had advised him that doing so would result in a minimum ninety-nine-year sentence. See id. at 1529-30. Lynch has not established such a probability here, and thus his claim fails.

B. Not Filing a Motion to Suppress the Murder-Suicide Letter

Lynch also contends that his trial counsel were ineffective for failing to file a motion to suppress the murder-suicide letter on Fourth Amendment grounds and prevent it from being used at the sentence stage.8 He argues that counsel should have challenged the police's entry into the Lynches' home as an unreasonable search. The Florida Supreme Court denied the claim. See Lynch, 2 So.3d at 68. It determined that Mrs. Lynch's sworn deposition testimony established that: (1) the police officers had consent to enter the Lynches' home, (2) the officers already knew about the murder-suicide letter because Mrs. Lynch had told the 911 operator about it, and (3) she was reading the letter in front of the officers when they asked her for it. Id. The court concluded that those facts showed that the officers were lawfully present in the home when they saw the letter and had probable cause to believe it was evidence of a crime — so the seizure was lawful under the plain view doctrine. See id.

As with all ineffective assistance claims, Lynch has the burden of showing that his counsel's performance (or non-performance) was both deficient and prejudicial. See Green v. Nelson, 595 F.3d 1245, 1251 (11th Cir.2010). To establish prejudice based on his attorneys' failure to seek suppression, Lynch has the more specific burden of demonstrating "that (1) the underlying Fourth Amendment issue has merit and (2) there is a `reasonable probability that the verdict would have been different absent the excludable evidence.'" Id. at 1251-52 (quoting Kimmelman v. Morrison, 477 U.S. 365, 375, 106 S.Ct. 2574, 2583, 91 L.Ed.2d 305 (1986)). Because it is dispositive, we will focus on the question of whether the underlying Fourth Amendment issue has merit.9

Lynch has not established the merits of his claim that the officers' entry into the Lynches' home was an unconstitutional search. Police may search a home without a warrant if they "obtain the voluntary consent of an occupant who shares, or is reasonably believed to share, authority over the area." Georgia v. Randolph, 547 U.S. 103, 106, 126 S.Ct. 1515, 1518, 164 L.Ed.2d 208 (2006). The Florida Supreme Court determined that the officers had consent to enter the Lynches' home, see Lynch, 2 So.3d at 68, and that determination is not objectively unreasonable, see 28 U.S.C. § 2254(d)(2). As the district court pointed out, Mrs. Lynch's deposition "does not explicitly state whether she invited the police into her home," but it supports a finding that she did. Lynch, 897 F.Supp.2d at 1313. Mrs. Lynch testified that she called 911, told them that her husband claimed to have killed someone, and asked them to investigate. Id. She also explained that, when the officer asked her for the letter, she "thought he was there to investigate or something." At the state post-conviction hearing, lead trial counsel testified that "my understanding [was] the search of the home occurred first while they're still on the phone with him, or shortly thereafter, and the wife is home and she gives them permission to enter." Together, those statements support the Florida Supreme Court's factual determination that the police got Mrs. Lynch's consent before entering the home. Lynch does not point to anything in the record that shows that determination was objectively unreasonable, which is his burden as a habeas petitioner. See Green, 595 F.3d at 1251. His failure to do so is fatal to his claim.

C. Investigation of Brain Impairment Evidence

Lynch also claims that his trial attorneys were ineffective for not discovering and presenting evidence that he suffers from a brain impairment, and if they had, there is a reasonable probability that he would not have been sentenced to death. To better understand this issue, we first explain in detail the expert opinion evidence that trial counsel discovered, that which they presented at the sentence stage, and the additional expert opinion evidence that collateral counsel discovered and presented in Lynch's state post-conviction proceedings.

1. Counsel's Investigation, the Expert Testimony at the Sentence Stage, and the Testimony at the State Post-Conviction Hearing

The first expert Lynch's attorneys hired in preparation for the sentence hearing was Dr. David Cox, a clinical neuropsychologist. See Lynch, 2 So.3d at 74. After examining Lynch, he diagnosed him with cognitive disorder NOS (not otherwise specified) and a possible paranoid personality disorder. Id. Dr. Cox's report also noted that Lynch might have a "cerebral dysfunction" and recommended neuropsychological testing to determine if he did. See id.

Trial counsel were not satisfied with Dr. Cox's report, so they brought in Dr. Olander, a forensic neuropsychologist, to evaluate Lynch. Id. While they told Dr. Olander that Dr. Cox had already evaluated Lynch, they did not tell her that his "cognitive testing suggest[ed] possible cerebral dysfunction in the form of significant right hemisphere weakness." See id. Nor did they mention that Dr. Cox had recommended neuropsychological testing "to determine if there is further deficiency not detected by the intelligence and memory screening testing already conducted." See id.

Based on her personal respect for Dr. Cox and her belief that trial counsel would have informed her if Dr. Cox had found any signs of impairment, Dr. Olander assumed that he had already ruled out cognitive impairment. Id. As a result, she did not perform any neuropsychological testing, but limited her evaluation to psychological testing and diagnosed Lynch with a schizoaffective disorder. Id. Dr. Olander testified at the sentence hearing "that Lynch did not have any brain impairment." Id.

Through his collateral counsel, Lynch presented evidence at his state post-conviction hearing that he had a brain impairment. Five mental health experts testified for Lynch at that hearing. Dr. Cox testified that Lynch "had a dysfunction of thinking skills, `quite likely due to a brain damage situation.'" Lynch, 897 F.Supp.2d at 1300.

Dr. Olander testified at the hearing that she had not tested Lynch for brain damage before the sentence stage of his trial based partly on her assumption that his trial counsel would have informed her if Dr. Cox had recommended doing that. Id. She then explained that if she had known Lynch had brain damage it would have changed her testimony at the sentence hearing. She would have instead testified that brain damage "would have had a significant impact on [Lynch's] self control and would have added weight to the emotional state [he] was experiencing at the time of the murders." Id.

Dr. David McCraney, a neurologist, testified at the state post-conviction hearing that Lynch "had frontal lobe and right hemisphere brain damage and suffered from psychosis." Id. He said that Lynch had likely suffered from those conditions his entire life, but that certain "stressors" — such as the credit card debt and his failing marriage — could have undermined Lynch's "ability to compensate for his cognitive impairment." Id. Dr. McCraney called Lynch's combination of brain impairment and emotional stressors "the perfect storm." Id. at 1303 n. 4.

Dr. Joseph Wu, a psychiatrist, testified at the state post-conviction hearing that after analyzing PET scans of Lynch's brain he had identified "an abnormality in the distribution of activity in the frontal lobe of the brain relative to the back of the brain." Id. at 1300. Finally, Dr. Joseph Sesta, a neuropsychologist, testified that Lynch "suffered from mild brain impairment and possible psychosis." Id. He criticized the testing that the State's mental health expert, Dr. Riebsame, did before the sentence hearing for failing to follow proper testing protocol. See id. at 1301. Dr. Sesta concluded that Lynch's ability to conform his conduct to the law was substantially impaired, but he did not offer an opinion about whether Lynch suffered from an extreme emotional disturbance. See id. at 1300-01.10

The State countered Lynch's new expert testimony at the state post-conviction hearing with two witnesses of its own: Dr. Riebsame and psychiatrist Dr. Jeffrey Danziger. Testifying to the same findings and opinion he had at the sentence hearing, Dr. Riebsame explained that he did not find any signs of psychotic or delusional thinking when he listened to the tape of Lynch's 911 call, or when he viewed the videotape of Lynch's post-arrest interview, or when he interviewed Lynch. Dr. Riebsame concluded that Lynch understood the criminality of his actions and that his "ability to conform his conduct to the law was not substantially impaired." Id. at 1301.

Dr. Danziger testified at the state post-conviction hearing that the planning and control Lynch had demonstrated in carrying out the murders and then deciding to back out of his suicide plan showed that he was able to control his impulses. Id. Dr. Danziger also concluded that "even if [Lynch] had a mild cognitive impairment, such an impairment would not have affected his behavior at the time of the murders," and that his ability to conform his conduct to the law was not substantially impaired when he committed the murders. Id.

2. Lynch's Challenge Based on Counsel's Investigation

Lynch contends that the district court erred in denying his ineffective assistance claim based on trial counsel's failure to obtain and present expert evidence that he suffers from a brain impairment. To succeed on this claim, Lynch must show that his counsel's failure to do so was (1) objectively unreasonable under the circumstances and (2) prejudicial to his defense. Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674 (1984). We begin by discussing the state court's decision and explaining why it deserves deference under 28 U.S.C. § 2254.

a.

The Florida Supreme Court denied this ineffective assistance claim on prejudice grounds. After deciding that the investigation into mitigating circumstances was deficient because trial counsel knew from Dr. Cox's report that "Lynch suffered from some type of cognitive impairment," yet they "never fully investigated this condition," the Florida Supreme Court concluded that trial counsel's failure did not prejudice Lynch because the statutory aggravating factors still far outweighed the mitigating factors. Lynch, 2 So.3d at 75-77. It found the testimony of the State's witness, Dr. Danziger, to be "the most persuasive" of all the expert testimony offered in the post-conviction proceeding because it was grounded in the facts of the murder and explained how those facts showed "planning, forethought, [and] organization, not impulsive action." Id. at 75-76. At the end of its four-page discussion of Lynch's new mental health evidence, the Florida Supreme Court concluded:

Id. at 77.

Although it ultimately concluded that Lynch had failed to establish the prejudice element of his ineffective assistance claim, the district court first determined that the Florida Supreme Court's decision that there was no prejudice was not entitled to § 2254(d) deference. See Lynch, 897 F.Supp.2d at 1303. It did so based entirely on its conclusion that the first sentence in the paragraph quoted above — the "failed to present any evidence" sentence — was an objectively unreasonable factual determination. See id.; see also 28 U.S.C. § 2254(d)(2). The district court deemed that factual determination unreasonable because of testimony from Drs. Olander, McCraney, and Sesta, which the court believed did link the type of brain impairment those experts found in Lynch to an inability to conform his behavior to the law. See Lynch, 897 F.Supp.2d at 1303.

Although it reached the right result anyway, the district court erred in getting there. It erred by not giving the Florida Supreme Court's decision on the prejudice element the deference that § 2254(d) requires. The "failed to present any evidence" sentence in the state court's opinion comes at the beginning of a paragraph that explains it, and it comes at the end of four pages of analysis of the new mental health evidence. See Lynch, 2 So.3d at 73-77. Lifting that one sentence off the page and interpreting it in isolation is inconsistent with the approach required by § 2254(d), one that imposes a "highly deferential standard for evaluating state-court rulings, which demands that state-court decisions be given the benefit of the doubt." Woodford v. Visciotti, 537 U.S. 19, 24, 123 S.Ct. 357, 360, 154 L.Ed.2d 279 (2002) (citation and quotation marks omitted). We have repeatedly cautioned against "overemphasis on the language of a state court's rationale" which "would lead to a `grading papers' approach that is outmoded in the post-AEDPA era." Ferguson v. Sec'y, Fla. Dep't of Corr., 716 F.3d 1315, 1337 (11th Cir.2013) (quoting Parker v. Sec'y for Dep't of Corr., 331 F.3d 764, 785 (11th Cir.2003)). The district court took the "grading papers" approach by red-inking the language in that one sentence without considering its context in the Florida Supreme Court's four-page discussion of Lynch's new mental health evidence. See Lynch, 897 F.Supp.2d at 1303 (interpreting Lynch, 2 So.3d at 73-77).

When we read that one sentence in the context of the entire paragraph and as part of the larger four-page discussion, giving the state court the benefit of the doubt that AEDPA requires, we conclude that what the court actually found was that Lynch's experts' generalized testimony (that his brain impairment rendered him unable to control his impulses) could not be squared with the facts of the case. In the three sentences following the one in question, the Florida Supreme Court explained what it meant. It said that there was "little to no testimony establishing that any impairment or schizoaffective symptoms contributed to [Lynch's] actions on [the day of the murders]." Lynch, 2 So.3d at 77. There was little or no evidence of a link because: "Lynch had no prior history of criminal activity but by all defense accounts has always had this condition. Furthermore, he thoroughly planned and carried out his memorialized intent to murder Roseanna Morgan and then demonstrated critical impulse control by refusing to commit suicide." Id. The Florida Supreme Court cited one of its decisions for the proposition that facts showing "an element of planning ... are inconsistent with" claims that the defendant was acting under "an extreme mental or emotional disturbance" during the murder. Id. (quoting Hoskins, 965 So.2d at 17-18).

And that is not all. There are other indications in the state court opinion of what the sentence in question means. First, the paragraph introducing the four-page analysis of the new mental health evidence frames the discussion that follows with this assessment: "Lynch has not connected any cognitive impairment to the events of [the day of the murder], which, in contrast, reveal a carefully crafted murder plot." Id. at 73. In other words, Lynch did not produce evidence explaining how, given the circumstances of the crime and the facts surrounding it, his "carefully crafted murder plot" could be the result of psychosis, brain damage, or any of the other mental problems his experts said he had.

Not only that, but in reviewing the new mental health evidence, the Florida Supreme Court specifically noted the expert testimony that the district court thought it had failed to note. The district court justified its conclusion that the Florida Supreme Court's factual determination was objectively unreasonable by citing statements from the testimony of Drs. Olander, McCraney, and Sesta. See Lynch, 897 F.Supp.2d at 1303 (citing testimony from those three doctors as proof that the Florida Supreme Court made an unreasonable factual determination). The district court's point was that the Florida Supreme Court must have overlooked those cited statements from the experts' testimony, all of which supported mitigating circumstances. See id. Instead of overlooking them, the Florida Supreme Court explicitly acknowledged those very statements in its review of the evidence. It stated that:

Lynch, 2 So.3d at 75. It went on to explain that Dr. Danziger's testimony was much more persuasive than the testimony from Lynch's experts because Dr. Danziger accounted for the actual facts of the murders. It also explained that the planning and organization that Lynch used to commit the murders undermined his claim that his actions were attributable to a brain impairment. See id. at 75-76.11 In concluding that the Florida Supreme Court overlooked Lynch's experts' testimony, the district court itself overlooked the Florida Supreme Court's discussion of that testimony. See Ferguson, 716 F.3d at 1340 ("AEDPA's command that we give state courts the benefit of the doubt ... means, at the least, that we should avoid finding internal inconsistencies and contradictions in the decisions of state courts where they do not necessarily exist.") (quotation marks omitted).

Perhaps it would have been clearer, and easier for us, if the "failed to present any evidence" sentence in the Florida Supreme Court's opinion had instead said that Lynch had "failed to present any persuasive evidence connecting any cognitive condition to his behavior." But AEDPA does not require that state courts write every sentence in their opinions with maximum clarity to simplify our task. Instead, it requires that we give state courts the benefit of the doubt and resolve ambiguities in their opinions in favor of their judgments, not against them. See id.

When the Florida Supreme Court's assessment of the expert testimony is looked at in the light that AEDPA requires, it is far from unreasonable. None of Lynch's experts squarely addressed his conduct and statements before, during, and after the murders and explained how they could be squared with a diagnosis of brain impairment. The district court's reasoning does not dissuade us from our conclusion. Its opinion focused on three general statements about brain impairment that were taken from the testimony of three of Lynch's testifying experts. See Lynch, 897 F.Supp.2d at 1303. Considering each of those statements against the undisputed historical facts shows that, just as the Florida Supreme Court recognized, none of Lynch's experts explained how their diagnosis of brain impairment could be squared with Lynch's conduct and statements before, during, and after the murders.

First, Dr. Olander made the general observation that: "The interaction of [brain damage and psychotic disorders] can be incredibly disabling for the individual." Of course. But she never explained how Lynch, if he was "incredibly disabl[ed]" could have carefully planned and carried out the murder of Morgan, as he did. Nor did she point to a single fact evidencing that Lynch actually was "incredibly disabl[ed]" when he committed the murders.

Dr. McCraney was given a hypothetical approximating Lynch's situation and replied that it was "more likely than not the brain impairment did contribute to the crime itself."12 But when the attorney for the State asked him if his opinion accounted for the facts of the murders, Dr. McCraney clarified that his opinion was based on Lynch's "constant conditions," not on his actual conduct during the murders. In other words, in reaching his opinion about what may have contributed to the crime, this expert failed to consider the facts leading up to the crime, the facts of the crime, and the facts about what Lynch did and said after the crime. Unlike Lynch's expert witnesses, state courts and federal courts must consider all of the relevant facts. The Florida Supreme Court did, and so do we.

Finally, Dr. Sesta testified that in his opinion Lynch's brain impairment left him "less able to conform his behavior to the standards of the law than a normal individual," and that people with Lynch's condition can behave normally for long periods of time until emotional stressors trigger a "disaster." But what about the critical facts involving Lynch's conduct leading up to, during, and after the crime? Dr. Sesta used the ostrich technique to deal with them. He simply did not bother to find out what they were. He testified that he didn't even know what the facts surrounding the murders were, and he never even attempted to analyze Lynch's state of mind during the crimes.

Given that none of Lynch's experts accounted for Lynch's conduct before, during, and just after the murders, the Florida Supreme Court's factual determination that Dr. Riebsame's testimony was more credible is a reasonable one within the meaning of § 2254(d)(2). That factual determination cannot be used as a basis for not granting § 2254(d) deference to the Florida Supreme Court's decision.

b.

As our previous discussion about the expert testimony going to the prejudice issue implies, the Florida Supreme Court's decision rejecting this ineffective assistance claim was not an unreasonable application of clearly established federal law. See 28 U.S.C. § 2254(d)(1).

Prejudice in the context of the sentence stage of a capital trial is gauged in terms of the mix of aggravating and mitigating circumstances. See Boyd v. Comm'r, Ala. Dep't of Corr., 697 F.3d 1320, 1341 (11th Cir.2012). We ask whether "without the errors, there is a reasonable probability that the balance of aggravating and mitigating circumstances would have been different." Bolender v. Singletary, 16 F.3d 1547, 1556-57 (11th Cir. 1994). The answer comes from taking the mitigating circumstances that were presented and adding to them the ones that should have been but were not, and then considering the total mitigating circumstances against all of the aggravating circumstances. See Porter v. McCollum, 558 U.S. 30, 41, 130 S.Ct. 447, 453-54, 175 L.Ed.2d 398 (2009); Holsey, 694 F.3d at 1268.

The death sentence imposed on Lynch for Morgan's murder was based in large part on the cold, calculated, and premeditated aggravating circumstance, while the death sentence imposed for Caday's murder was based in large part on the heinous, atrocious, or cruel aggravating circumstance. See Lynch, 841 So.2d at 368; Fla. Stat. § 921.141(5)(h), (i). Those "are two of the most serious aggravators set out in [Florida's] statutory sentencing scheme." Larkins v. State, 739 So.2d 90, 95 (Fla. 1999); see also Buzia v. State, 926 So.2d 1203, 1216 (Fla.2006) (same). And they both accurately characterized the extreme circumstances of the two murders. See supra Parts I-II.

Those are not, however, the only aggravating circumstances on which the sentencing judge based the death sentences. For the murder of Morgan, as well as for the murder of Caday, the judge also found and relied on the aggravating circumstance that Lynch "had previously been convicted of a violent felony" and the aggravating circumstance that he had committed the murder "while ... engaged in committing one or more other felonies." Lynch, 841 So.2d at 368 (applying Fla. Stat. § 921.141(5)(b) & (d)).

Against the three aggravating circumstances supporting each death sentence, the only statutory mitigating circumstance was the one for "no significant history of prior criminal activity." See id. at 368 & n. 5. There were also eight non-statutory mitigating circumstances. Id. To make a difference, Lynch's new brain impairment evidence would have to alter the balance between the aggravating and mitigating circumstances. See Ponticelli v. Sec'y, Fla. Dep't of Corr., 690 F.3d 1271, 1300 (11th Cir.2012); Sochor v. Sec'y Dep't of Corr., 685 F.3d 1016, 1030 (11th Cir.2012). The Florida Supreme Court determined that the new evidence would not have altered the balance because the theory that Lynch suffered from a brain impairment that affected his conduct could not be squared with the fact that he "displayed organized, methodical planning in his perpetration of these offenses," "displayed critical impulse control in electing not to inflict self-harm," and "explained his actions in a detailed, specific fashion" both during and after the crimes. Lynch, 2 So.3d at 73, 76-77. The new evidence, in essence, adds little of value on the mitigation side of the scale.

The Florida Supreme Court's holding that Lynch failed to carry his burden of proving prejudice is objectively reasonable. We reached the same conclusion about that court's holding in another case involving similar circumstances. See Rutherford v. Crosby, 385 F.3d 1300, 1316 (11th Cir. 2004). In that case, the § 2254 petitioner had planned and carried out the robbery and murder of an elderly widow. See id. at 1302. He contended that his counsel had rendered ineffective assistance by failing to present expert opinion testimony in the sentence stage showing that, as one expert put it, the petitioner had committed the murder while "under the influence of `stressors' because of his drinking and getting back together with his wife." Id. at 1314, 1316. Applying AEDPA deference, we held that reasonable jurists could conclude, as the Florida Supreme Court did, that there was no reasonable probability such mental state mitigation evidence would have altered the result given the evidence that the petitioner had planned and deliberately carried out the murder in a cold and calculated way. Id.

The same reasoning applies here. The prosecution's overwhelming evidence proving that the murders were committed in a calculated, premeditated, and deliberate manner undercuts the new evidence that he may have been mentally impaired at the time of the two murders. Reasonable jurists could conclude, as the Florida Supreme Court did, that the strong aggravating circumstances would still have outweighed all of the mitigating circumstances. For that reason, Lynch's claim fails.13

VII.

In its direct appeal, the State contends that the district court erred in granting Lynch habeas relief on his claim that he was denied effective assistance of counsel when his attorneys advised him to waive his right to a sentence-stage jury before adequately investigating and advising him about his brain impairment as a potential mitigating factor. See Lynch, 897 F.Supp.2d at 1306-09. The Florida Supreme Court held that trial counsel had not performed deficiently because they made a reasonable strategic decision to avoid what counsel felt would almost certainly be an emotional jury in favor of a potentially "less emotional, highly experienced judge." Lynch, 2 So.3d at 71. It also held that Lynch was not prejudiced because his "asserted ignorance of ... a comparatively minor mental-health diagnosis could not have affected his decision to waive a penalty-phase jury." Id. at 70.

The district court disagreed with both of the state court's holdings. First, it determined that counsel's advice could not be a reasonable strategic choice because it was based in part on counsel's deficient investigation into mental health mitigation evidence. See Lynch, 897 F.Supp.2d at 1308. The district court also concluded that the Florida Supreme Court's prejudice determination had "unreasonably discounted the weight and the importance of the available mental health mitigation of which Petitioner was not apprised prior to his waiver of a jury." Id. at 1309 (citing 28 U.S.C. § 2254(d)(2)). That conclusion was based on the district court's reading of the "failed to present any evidence" sentence in the Florida Supreme Court's discussion of Lynch's failure-to-investigate claim. See id. (citing id. at 1303). For reasons we have already discussed at length, the district court misread that sentence. See supra Section VI.C.2.a. It should not have cast aside the § 2254(d) deference owed to the Florida Supreme Court's decision on this issue.

After conducting a de novo review of the record, the district court concluded that Lynch had been prejudiced. See id. at 1309. Its belief that there was a reasonable probability that Lynch would have opted for a sentence-stage jury but for trial counsel's deficient performance was based on three things: (1) at the state post-conviction hearing, lead trial counsel testified "that brain damage is a compelling mitigator for a jury to consider"; (2) Lynch's mental health was "the only weighty mitigating factor in his defense"; and (3) in a letter to trial counsel, Lynch had "expressed concern that Judge Eaton would be harsher in sentencing than the judge initially assigned to the case." Id. None of those three factors speak directly to the question of whether a jury might have been more favorable to Lynch than a judge, and thus none of them support the conclusion that if Lynch had been informed of the mental state mitigating evidence he would have rejected his counsel's advice to waive a jury at the sentencing stage. We will discuss that more in a moment.

We decide this claim on the prejudice issue.14 In doing so, we assume — without deciding — that Lynch's ineffectiveness claim is governed by the prejudice standard from Hill v. Lockhart, 474 U.S. 52, 58-59, 106 S.Ct. 366, 370, 88 L.Ed.2d 203 (1985). The Hill decision requires a petitioner claiming that he pleaded guilty based on his trial counsel's deficient advice to show "a reasonable probability that, but for counsel's errors, he would not have pleaded guilty and would have insisted on going to trial." Id. at 59, 106 S.Ct. at 370. It is not entirely clear that Hill applies where, as here, the ineffective assistance claim is based on counsel's advice to waive a jury at a sentence hearing, instead of on advice to plead guilty and waive a trial on guilt.

In similar circumstances, two of our sister circuits have applied Strickland's prejudice standard instead of Hill's and asked if there was a reasonable probability that the ultimate outcome of the proceeding would have been different. See United States v. Lilly, 536 F.3d 190, 195-96 (3d Cir.2008) (applying Strickland to counsel's advice to opt for a bench trial in the guilt stage); Jells v. Mitchell, 538 F.3d 478, 510-11 (6th Cir.2008) (applying Strickland to counsel's advice to waive a jury at the guilt and sentence stages of a capital trial). But here both the Florida Supreme Court and the district court applied Hill's prejudice standard, see Lynch, 2 So.3d at 57, 70-71; Lynch, 897 F.Supp.2d at 1308-09, and Lynch urges us to do so as well. Because of that, we will assume for purposes of this case, as the parties both contend, that Hill applies.

Hill instructs courts that, where a petitioner faults counsel for advising him without first finding and informing the petitioner about evidence relevant to that advice, the prejudice determination "will depend on the likelihood that discovery of the evidence would have led counsel to change his recommendation."15 474 U.S. at 59, 106 S.Ct. at 370. Assessing that likelihood "will depend in large part on a prediction whether the evidence likely would have changed the outcome" with a jury recommending a sentence to the judge as opposed to a judge determining a sentence without a jury's recommendation.16 Id. To justify habeas relief on this portion of his claim, Lynch must establish that the Florida Supreme Court's prejudice analysis is either "contrary to" or "an unreasonable application of" clearly established federal law. 28 U.S.C. § 2254(d)(1).

A state court decision "is not contrary to federal law unless it contradicts the United States Supreme Court on a settled question of law or holds differently than did that Court on a set of materially indistinguishable facts." Evans v. Sec'y, Dep't of Corr., 703 F.3d 1316, 1325 (11th Cir.2013) (en banc) (quotation marks omitted). The Florida Supreme Court's decision did neither. It applied an objective form of prejudice analysis that focused on two things: (1) how the "comparatively minor mental-health diagnosis" from Lynch's new expert evidence would not have affected the balance of aggravating and mitigating circumstances, and (2) Lynch's failure to offer any reason to conclude that a jury would be more receptive to that evidence than "a potentially less emotional, highly experienced jurist." Lynch, 2 So.3d at 71. The Supreme Court has not held that courts applying Hill's prejudice standard must determine what the particular petitioner or his attorney would have done if the additional evidence had been discovered. And Hill itself teaches that prejudice determinations based on the "predictions of the outcome at a possible trial ... should be made objectively."17 474 U.S. at 59-60, 106 S.Ct. at 371; see also Pilla v. United States, 668 F.3d 368, 373 (6th Cir.2012) ("The [Hill] test is objective, not subjective...."). Thus, the state court decision was not contrary to clearly established federal law.18

Nor was the Florida Supreme Court's prejudice analysis an "unreasonable application of" clearly established federal law. A state court decision is not an unreasonable application of federal law unless the petitioner shows that there is no possibility that "fairminded jurists" could debate whether the state court's decision is inconsistent with the holding of a prior Supreme Court decision. Evans, 703 F.3d at 1326 (quotation marks omitted). Here, the analysis turned on two factors. The first factor was the Florida Supreme Court's determination that the new brain impairment evidence would not have affected the balance of aggravating and mitigating circumstances because: (1) the new evidence established only that Lynch had a "mild cognitive impairment"; (2) that impairment "ha[d] not affected his ability to lead an otherwise normal life"; (3) he was "of average overall intelligence"; and (4) he had "never connected this `impairment' to his actions on March 5, 1999." Lynch, 2 So.3d at 70-71. That was not an unreasonable assessment. As we already explained when analyzing Lynch's failure-to-investigate claim, the facts of the crime and the expert testimony offered by the State effectively undercut the brain impairment testimony of Lynch's experts. See supra Section VI.C.2.

The second factor in the Florida Supreme Court's prejudice analysis was Lynch's failure to offer any reason to think the jury would have been more receptive than the judge to the brain impairment evidence so that the new evidence "would have altered his decision to forgo a penalty-phase jury in favor of a potentially less emotional, highly experience jurist." Lynch, 2 So.3d at 71. Neither Lynch's brief nor the district court's opinion offers any reason why a jury would be more likely than a judge to be persuaded by such evidence, let alone a reason with which no "fairminded jurists" could disagree. See Evans, 703 F.3d at 1326 (quotation marks omitted). The Florida Supreme Court's prejudice analysis was therefore not an unreasonable application of clearly established federal law.

Nor do the three things that the district court relied on in its de novo determination that there was prejudice overcome the § 2254(d) deference owed to the Florida Supreme Court's determination. See Lynch, 897 F.Supp.2d at 1309. None of them speaks directly to "whether the evidence likely would have changed the outcome" with a jury and a judge as opposed to a judge alone, which Hill identifies as the primary factor in its prejudice inquiry. 474 U.S. at 59, 106 S.Ct. at 370. Fairminded jurists could agree with the state court's reasoning and disagree with the district court's. See Evans, 703 F.3d at 1326.

The district court focused first on lead trial counsel's "admission that brain damage is a compelling mitigator for a jury to consider." Lynch, 897 F.Supp.2d at 1309. Counsel's testimony at the state post-conviction hearing was that juries are "more receptive to a mitigator like brain damage than they are to the common scheme of poor upbringing and mental illness." But that testimony simply reflects the fact that, as counsel put it, "showing a physical defect of the brain" is often more persuasive than "showing something amorphous like a mental illness." Counsel never suggested that juries are more receptive than judges to brain impairment evidence, which is what matters here.

The district court also pointed out that Lynch's "mental health [w]as the only weighty mitigating factor in his defense" and that in two letters to trial counsel Lynch expressed interest in presenting mental health mitigation evidence. Id. Again, those statements speak to mental health mitigation generally, not to the relevant question of whether a judge or a jury would be more receptive to that mitigation. There is absolutely nothing in the record to support the proposition, which the district court apparently relied on, that juries would be more receptive than judges to mental health mitigation evidence.

Finally, the district court referred to Lynch's letter to trial counsel dated August 29, 2000, which discussed the fact that the judge who initially had been scheduled to preside over the trial had been replaced by Judge Eaton. Id. Expressing the hope that the new judge would not be harsher on sentencing, Lynch wrote: "Also the change of judge from Alley to O.H. Eaton I don't feel will help, he reminds me of a[] cranky old man & possibly harsher as concerning sentence. I hope not." Lynch's vague expression of concern does not make the Florida Supreme Court's prejudice determination objectively unreasonable. He chose to waive a sentence-stage jury despite his initial concern about Judge Eaton, and his worry that Judge Eaton might be harsher than Judge Alley does not directly answer the relevant question: Judge Eaton or a jury.19 As the Florida Supreme Court recognized, in Lynch's case the primary reason for choosing Judge Eaton instead of a jury was the likelihood that Judge Eaton would be less emotional and therefore more likely to fully and fairly consider any mitigation evidence. See Lynch, 2 So.3d at 47. That factor still favored choosing Judge Eaton even with the new mental health mitigation evidence. A reasonable jurist could conclude that Lynch was not prejudiced by his counsel's advice to waive the sentence-stage jury. The district court erred in granting Lynch sentence-stage relief on this claim.

VIII.

Because Lynch was not denied the effective assistance of counsel, the part of the district court's judgment denying habeas relief to Lynch is affirmed, and the part of the judgment granting him relief is reversed.

AFFIRMED in part and REVERSED in part.