CARNES, Chief Judge:

James Hitchcock, a Florida inmate sentenced to death for the strangulation murder of a thirteen-year-old girl, appeals the denial of his petition for a writ of habeas corpus under 28 U.S.C. § 2254. He contends that his Eighth and Fourteenth Amendment rights were violated at his latest resentencing proceeding when the state trial court refused to admit and consider, as relevant mitigating evidence, the prosecution's offer to recommend a life sentence in exchange for a guilty plea to first-degree murder, an offer that Hitchcock rejected. He also contends that counsel at the resentencing hearing was ineffective for failing to elicit testimony from the defense's mental health expert about the applicability of two statutory mitigating factors and for failing to seek a neuropsychological evaluation for the presence of possible brain damage.

I.

The lengthy and complicated history of this case dates back thirty-seven years. In the summer of 1976, Hitchcock raped his brother's thirteen-year-old stepdaughter and then strangled her to death after she threatened to report the sexual assault. He was indicted on a single count of first-degree murder and, after rejecting the prosecution's offer to recommend a life sentence in exchange for a guilty plea, was convicted at trial and sentenced to death. The Florida Supreme Court affirmed his conviction and capital sentence on direct appeal, see Hitchcock v. State, 413 So.2d 741 (Fla.1982), and the state courts rejected his initial attempts to obtain post-conviction relief, see Hitchcock v. State, 432 So.2d 42 (Fla.1983).

In May of 1983, Hitchcock filed a federal habeas petition under § 2254, which the district court denied and that denial was affirmed on appeal. See Hitchcock v. Wainwright, 770 F.2d 1514 (11th Cir.1985) (en banc). The Supreme Court, however, granted his petition for a writ of certiorari and vacated his death sentence because the penalty phase jury was instructed not to consider, and the sentencing judge refused to consider, evidence of non-statutory mitigating circumstances. See Hitchcock v. Dugger, 481 U.S. 393, 399, 107 S.Ct. 1821, 1824, 95 L.Ed.2d 347 (1987). Following his first resentencing proceeding, which again resulted in a sentence of death, Hitchcock challenged the state trial court's refusal to admit the prosecution's plea offer as relevant mitigating evidence at sentencing. The Florida Supreme Court rejected that challenge on appeal, concluding that the offer was not relevant mitigating evidence under the constitutional rule announced in Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978), because it had no bearing on Hitchcock's character, record, or the circumstances of his crime. Hitchcock v. State, 578 So.2d 685, 689-91 (Fla.1990), vacated on other grounds by Hitchcock v. Florida, 505 U.S. 1215, 112 S.Ct. 3020, 120 L.Ed.2d 892 (1992).

Hitchcock nevertheless managed to obtain two more penalty phase proceedings, each in its turn resulting in death sentences. After the third death sentence was vacated, see Hitchcock v. State, 673 So.2d 859, 860 (Fla.1996), the fourth and (so far) last sentencing hearing was conducted in September 1996. At that sentencing hearing, the defense called Dr. Jethro Toomer, a clinical and forensic psychologist, who testified that Hitchcock suffered from borderline personality disorder resulting in lifelong "personality difficulties," which would have affected him at the time of the murder by causing him to act impulsively. Dr. Toomer did not, however, diagnose Hitchcock with any major psychiatric disorder, nor was he specifically asked by defense counsel about the presence of two statutory mitigating circumstances — whether the crime was committed while Hitchcock was under the influence of extreme mental or emotional disturbance, and whether his capacity to appreciate the criminality of his conduct or conform his conduct to the law was substantially impaired. See Fla. Stat. § 921.141(6)(b), (f) (1996). Defense counsel did argue during closing arguments that Hitchcock was under the influence of extreme mental or emotional disturbance at the time of the offense.

In the 1996 resentencing proceeding, the jury recommended the death penalty by a vote of ten to two and the trial court followed that recommendation, finding that the aggravating circumstances of Hitchcock's crime outweighed the mitigating ones. The court found four statutory aggravating circumstances: (1) the crime was committed while Hitchcock was under a sentence of imprisonment; (2) he committed the crime while engaged in the felony of sexual battery; (3) the crime was committed for the purpose of avoiding arrest; and (4) the crime was especially heinous, atrocious, or cruel. The trial court found only one statutory mitigating circumstance, that Hitchcock was 20 years old at the time of the murder, and several non-statutory mitigating circumstances, which it gave comparatively little weight. The non-statutory mitigating circumstances found by the trial court included that Hitchcock was under the influence of lifelong personality difficulties at the time of the offense, that he suffered from borderline personality disorder, and that the offense resulted from an unplanned, impulsive act. The Florida Supreme Court affirmed the death sentence on appeal and, in doing so, again rejected Hitchcock's contention that the sentencing judge erred in excluding evidence of the prosecution's rejected plea offer. See Hitchcock v. State, 755 So.2d 638, 645 (Fla.2000). The court explained that the claim was barred because it had been considered and rejected on the merits during Hitchcock's appeal from his first resentencing proceeding. Id.

In 2001 Hitchcock filed a state motion for post-conviction relief from his latest death sentence, contending, among other things, that counsel at his sentencing proceeding was ineffective for failing to (1) specifically elicit testimony from Dr. Toomer about the presence of the two statutory mental health mitigators and (2) have him evaluated by a neuropsychologist for indications of organic brain damage. After holding an evidentiary hearing, which was marked by conflicting expert testimony about the presence, extent, and influence of possible brain damage, the state trial court rejected the claims of ineffective assistance of counsel on the merits.

The Florida Supreme Court affirmed the denial of post-conviction relief, concluding that Hitchcock was not prejudiced by his counsel's failure to ask Dr. Toomer for his ultimate opinion about the applicability of the statutory mental health mitigators in light of "the extensive mitigation that was presented" at resentencing, including Dr. Toomer's testimony that Hitchcock was experiencing the effects of borderline personality disorder at the time of the offense, and "the extremely weighty aggravators proven in this case." Hitchcock v. State, 991 So.2d 337, 356-58 (Fla. 2008). The Florida Supreme Court further found that counsel's failure to seek a neuropsychological evaluation was neither deficient nor prejudicial given the "conflicting expert testimony presented" during the post-conviction hearing, the speculative nature of Hitchcock's contention that he suffered from brain damage at the time of the murder, and the "extremely weighty" aggravating factors in the case. Id. at 360. The court also noted that several mental health experts had testified about "Hitchcock's normal intelligence, lack of mental illness, and positive adaptation to prison life." Id. at 360-61.

Hitchcock filed his current federal habeas petition in October 2008, reiterating his claims challenging his 1996 death sentence. The district court denied the § 2254 petition but granted Hitchcock a certificate of appealability (COA) on his claim that evidence of the prosecution's plea offer was improperly excluded during his last resentencing proceeding. We later expanded the COA to include Hitchcock's two claims of ineffective assistance of resentencing counsel.

II.

We review de novo the denial of a federal habeas petition. Jamerson v. Sec'y for Dep't of Corr., 410 F.3d 682, 687 (11th Cir.2005). Under the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), federal courts may not grant habeas relief on a claim adjudicated on the merits in state court unless the state court's decision "was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court." 28 U.S.C. § 2254(d)(1). The phrase "clearly established Federal law" refers only to the legal principles embodied in the holdings of the United States Supreme Court. See Thaler v. Haynes, 559 U.S. 43, 47, 130 S.Ct. 1171, 1173, 175 L.Ed.2d 1003 (2010); Putman v. Head, 268 F.3d 1223, 1241 (11th Cir.2001). And a state court's application of clearly established federal law cannot be deemed unreasonable unless "no `fairminded jurist' could agree" with the state court's conclusion. Holsey v. Warden, Ga. Diagnostic Prison, 694 F.3d 1230, 1257 (11th Cir.2012) (quoting Harrington v. Richter, ___ U.S. ___, 131 S.Ct. 770, 786, 178 L.Ed.2d 624 (2011)).

A.

Hitchcock contends that he was deprived of his constitutional right to present relevant mitigating evidence at his 1996 resentencing when the state trial court excluded from evidence and refused to consider the State's pretrial offer to recommend a life sentence in return for a guilty plea. Hitchcock insists that the plea offer, which he rejected, is relevant because it shows that the prosecution believed that a death sentence was not warranted in his case.

The Supreme Court has held that "the Eighth and Fourteenth Amendments require that the sentencer, in all but the rarest kind of capital cases, not be precluded from considering, as a mitigating factor, any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death." Lockett, 438 U.S. at 604, 98 S.Ct. at 2964-65 (plurality opinion); see also Eddings v. Oklahoma, 455 U.S. 104, 110, 102 S.Ct. 869, 874, 71 L.Ed.2d 1 (1982) (adopting the rule announced by the plurality in Lockett). The Court has emphasized, however, that this rule does not "limit[] the traditional authority of a court to exclude, as irrelevant, evidence not bearing on the defendant's character, prior record, or the circumstances of his offense." Lockett, 438 U.S. at 604 n. 12, 98 S.Ct. at 2965 n. 12.

This constitutional rule, and its associated limitation, reflects "the principle that punishment should be directly related to the personal culpability of the criminal defendant." Penry v. Lynaugh, 492 U.S. 302, 319, 109 S.Ct. 2934, 2947, 106 L.Ed.2d 256 (1989), abrogated on other grounds by Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). While the circumstances of a defendant's crime are related to his culpability, his "background and character [are also] relevant because of the belief, long held by society, that defendants who commit criminal acts that are attributable to a disadvantaged background, or to emotional and mental problems, may be less culpable than defendants who have no such excuse." Id. (quotation marks omitted). As framed by the Supreme Court, the question of constitutional relevance turns on whether the proffered mitigating evidence has "any tendency to mitigate the defendant's culpability" or might otherwise serve as a reasonable basis for imposing a sentence less than death. Tennard v. Dretke, 542 U.S. 274, 284-87, 124 S.Ct. 2562, 2570-71, 159 L.Ed.2d 384 (2004).

Although the mitigating circumstances standard is a broad one, it is not without boundaries. As Justice O'Connor pointed out in Franklin v. Lynaugh, "[n]othing in Lockett or Eddings requires that the sentencing authority be permitted to give effect to evidence beyond the extent to which it is relevant to the defendant's character or background or the circumstances of the offense." 487 U.S. 164, 185-86, 108 S.Ct. 2320, 2333, 101 L.Ed.2d 155 (1988) (O'Connor, J., concurring in the judgment). The decision in Franklin underscores that point. It held that the Constitution "in no way mandates reconsideration by capital juries, in the sentencing phase, of their residual doubts over a defendant's guilt," because "[s]uch lingering doubts are not over any aspect of petitioner's character, record, or a circumstance of the offense." Id. at 174, 108 S.Ct. at 2327 (plurality opinion) (quotation marks omitted). Likewise, a plea offer from the prosecutor is not evidence about "any aspect of petitioner's character, record, or a circumstance of the offense." Id.

The Sixth Circuit's recent en banc decision in United States v. Gabrion provides a helpful analogy. See 719 F.3d 511 (6th Cir.2013) (en banc). In that case the capital murder was committed inside the State of Michigan, which has no death penalty, but it was also committed 227 feet inside a National Forest, which subjected the defendant to the territorial jurisdiction of the United States and the federal death penalty. Id. at 515-18. The Sixth Circuit rejected the contention that the location of the murder was a mitigating circumstance, either because Gabrion committed it in a state that has no death penalty or because if he had committed it 228 feet away from where he did he would not have faced a death sentence. Id. at 520-24. The Court pointed out that the focus of the mitigating circumstances standard on the defendant's character, background, and the circumstances of his offense, particularly as they relate to the question of culpability, is reflected in the types of evidence that the Supreme Court has held to be mitigating: evidence of a defendant's youth, abusive upbringing, and emotional disturbance, see Eddings, 455 U.S. at 115, 102 S.Ct. at 877; evidence of a defendant's low IQ or impaired intellectual functioning, see Tennard, 542 U.S. at 287-88, 124 S.Ct. at 2571-72; evidence of a defendant's post-crime rehabilitation or good behavior in prison, see Skipper v. South Carolina, 476 U.S. 1, 4-5, 106 S.Ct. 1669, 1670-71, 90 L.Ed.2d 1 (1986); evidence of a defendant's military service and hardships suffered during it, see Porter v. McCollum, 558 U.S. 30, 39-40, 130 S.Ct. 447, 453, 175 L.Ed.2d 398 (2009); evidence of a defendant's religious conversion while in prison, see Wong v. Belmontes, 558 U.S. 15, 21, 130 S.Ct. 383, 387, 175 L.Ed.2d 328 (2009); evidence that a defendant was intoxicated at the time of the crime, see Parker v. Dugger, 498 U.S. 308, 314, 111 S.Ct. 731, 736, 112 L.Ed.2d 812 (1991); and evidence that the defendant played a minor role in the offense, see Enmund v. Florida, 458 U.S. 782, 797-98, 102 S.Ct. 3368, 3376-77, 73 L.Ed.2d 1140 (1982). See Gabrion, 719 F.3d at 521. The facts those types of evidence show are relevant mitigating circumstances because they allow a sentencing judge or jury to express "a reasoned moral response to the defendant's background, character, and crime" in deciding whether to impose the ultimate punishment of death. See Penry, 492 U.S. at 319, 109 S.Ct. at 2947 (quotation marks omitted).

By contrast, the Supreme Court has held that a defendant has no constitutional right to present evidence of his innocence at sentencing because it sheds no light on his character, record, or the "manner in which he committed the crime for which he has been convicted." Oregon v. Guzek, 546 U.S. 517, 523, 126 S.Ct. 1226, 1230-31, 163 L.Ed.2d 1112 (2006). For similar reasons, some of our sister circuits have held that evidence of the impact that a defendant's execution will have on his family or friends, as well as evidence about his family's love for him, is not mitigating circumstance evidence because it does not reflect on the defendant's background or character or the circumstances of the crime. See United States v. Hager, 721 F.3d 167, 194-97 (4th Cir.2013); United States v. Snarr, 704 F.3d 368, 401-02 (5th Cir.2013); Stenson v. Lambert, 504 F.3d 873, 891-92 (9th Cir.2007); Coleman v. Saffle, 869 F.2d 1377, 1393 (10th Cir.1989).

The fact that Hitchcock would not have received a death sentence if only he had accepted the plea offer has as little or nothing to do with his character, record, or the circumstances of the offense, and is as devoid of any moral significance as the fact that Gabrion would not have faced a death sentence if only he had murdered the victim in a different location. Just as "mitigation under the Eighth Amendment is not a matter of geographic coordinates," Gabrion, 719 F.3d at 522, neither is it a matter of a particular prosecutor's willingness to bargain.

The Supreme Court has never held that a prosecutor's offer to take the death penalty off the table in return for a guilty plea is a mitigating circumstance. And all but one of the courts to have decided the issue have held that failed plea negotiations and rejected plea offers are not mitigating circumstances because they have no bearing on a defendant's character or record or the circumstances of the offense. See Owens v. Guida, 549 F.3d 399, 419-20 (6th Cir. 2008) (holding that evidence of failed plea negotiations is not relevant to mitigation because it has no bearing on the defendant's character, record, or the circumstances of his offense); Bennett v. State, 933 So.2d 930, 953 (Miss.2006) (holding that a capital defendant was not entitled to present evidence of a plea offer for a life sentence because it was "neither mitigation evidence of his character nor part of the circumstances of the crime for which [he] was convicted"); Howard v. State, 367 Ark. 18, 238 S.W.3d 24, 47 (2006) (same); Neal v. Commonwealth, 95 S.W.3d 843, 852-53 (Ky.2003) (holding that a plea offer does not constitute relevant mitigating evidence because it "is not an aspect of the character of the defendant, nor is it a circumstance of the offense, or a mitigating aspect of the record of the defendant"); Wisehart v. State, 693 N.E.2d 23, 64 (Ind. 1998) (same); Wiggins v. State, 324 Md. 551, 597 A.2d 1359, 1370 (1991) (same), reversed on other grounds by Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003); Ross v. State, 717 P.2d 117, 122 (Okla.Cr.App.1986) (holding that a capital defendant had no right to present, as mitigating circumstance evidence, a negotiated plea agreement that was later withdrawn). But see Scott v. Schriro, 567 F.3d 573, 584 (9th Cir.2009) ("The plea offer's mitigatory effect is clear: the prosecution thought this was not a clear-cut death penalty case.").

We agree with the seven courts (we make it eight) on the majority side of this issue and not with the Ninth Circuit, which is a minority of one. Evidence of a rejected plea offer for a lesser sentence, like evidence of innocence or evidence of the geographical location of the crime, is not a mitigating circumstance because it sheds no light on a defendant's character, background, or the circumstances of his crime. Such a plea offer does not by itself show that the prosecutor believed the defendant did not deserve the death penalty.1 A plea offer of a non-capital sentence in a capital case may simply reflect a desire to conserve prosecutorial resources, to spare the victim's family from a lengthy and emotionally draining trial, to spare them the possibility of protracted appeal and post-conviction proceedings (spanning in this case more than three decades), or to avoid any possibility, however slight, of an acquittal at trial.

Even if one could somehow infer from a plea offer that a particular prosecutor's personal views were that the defendant did not deserve a death sentence as much as other murderers did, or even at all, that personal belief would not be admissible or relevant evidence. We have held that it is misconduct for a prosecutor to tell the jury that he personally believes the defendant deserves a death sentence. See Brooks v. Kemp, 762 F.2d 1383, 1410 (11th Cir.1985) (en banc) (holding it improper to even imply "to the jury that the prosecutor's office had already made the careful judgment that this case, above most other murder cases, warranted the death penalty"), vacated on other grounds, 478 U.S. 1016, 106 S.Ct. 3325, 92 L.Ed.2d 732 (1986), reinstated, 809 F.2d 700 (11th Cir.1987) (en banc); Tucker v. Kemp, 762 F.2d 1496, 1505 (11th Cir.1985) (en banc) (holding that a prosecutor's "statement [to the capital sentencing jury], invoking the expertise of the prosecutor to suggest the special seriousness of the crime, was improper"); see also Drake v. Kemp, 762 F.2d 1449, 1459-60 (11th Cir.1985) ("An attorney's personal opinion is irrelevant to the task of a sentencing jury."). By the same token, a single prosecutor's personal belief that the defendant may not deserve the death penalty as much as some other murderers, or at all, should not be put before the jury. It is just as irrelevant as a prosecutor's personal opinion running the other way.

To the extent Hitchcock's argument is that his rejection of the plea offer is relevant to the question of whether he is innocent of the crime because it shows that he was willing to face death rather than admit guilt, the Supreme Court has expressly rejected the notion that evidence of a defendant's innocence, or of residual doubt about his guilt, is constitutionally relevant at sentencing. See Guzek, 546 U.S. at 523, 126 S.Ct. at 1230-31; Franklin, 487 U.S. at 174, 108 S.Ct. at 2327 (plurality opinion).

For what it is worth, we also note that a constitutional rule requiring the admission of rejected plea offers as mitigating evidence in capital cases could have the pernicious effect of discouraging prosecutors from extending plea offers in the first place, lest those offers come back to haunt them at sentencing. See Wright v. Bell, 619 F.3d 586, 600 (6th Cir.2010) ("Allowing a defendant to use plea negotiations in mitigation would clearly discourage plea negotiations in capital cases as prosecutors would correctly fear that during the second stage proceedings, they would be arguing against themselves.") (quotation omitted). That would be in no one's best interest.2

For these reasons, we hold that the Constitution does not mandate the admission of rejected plea offers as relevant mitigating evidence at sentencing. As a result, whether the issue is reviewed de novo or under AEDPA's deferential standards, Hitchcock is not entitled to federal habeas relief on his Eighth Amendment claim. This is the same type of dual holding that the Supreme Court reached in Knowles v. Mirzayance, 556 U.S. 111, 114, 129 S.Ct. 1411, 1415, 173 L.Ed.2d 251 (2009) ("Whether reviewed under the standard of review set forth in § 2254(d)(1) or de novo, [the petitioner] failed to establish that his counsel's performance was ineffective."). See also Berghuis v. Thompkins, 560 U.S. 370, 390, 130 S.Ct. 2250, 2265, 176 L.Ed.2d 1098 (2010) ("[A] habeas petitioner will not be entitled to a writ of habeas corpus if his or her claim is rejected on de novo review."); Reese v. Sec'y, Fla. Dep't of Corr., 675 F.3d 1277, 1291 (11th Cir. 2012) (explaining that, even when it is clear that AEDPA deference applies, we may affirm the denial of federal habeas relief based solely on de novo review); Allen v. Sec'y, Fla. Dep't of Corr., 611 F.3d 740, 753 (11th Cir.2010) ("Alternatively, even if no deference were due the state collateral trial court's decision on the performance element, we would conclude on de novo review that [the petitioner] had failed to establish it."). These are our two alternative holdings on this issue.3

B.

Hitchcock also contends that his lawyer during his latest resentencing proceeding was ineffective for failing to elicit testimony from defense expert Dr. Toomer about the applicability of the two statutory mental health mitigating factors, and for failing to seek a neuropsychological evaluation and present evidence of possible brain damage. A petitioner asserting a claim of ineffective assistance of counsel must demonstrate both deficient performance and prejudice — that counsel's performance "fell below an objective standard of reasonableness" and that "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, 687-88, 694, 104 S.Ct. 2052, 2064, 2068, 80 L.Ed.2d 674 (1984). Where, as here, a defendant challenges a death sentence, the prejudice inquiry asks "whether there is a reasonable probability that, absent the errors, the sentencer — including an appellate court, to the extent it independently reweighs the evidence — would have concluded that the balance of aggravating and mitigating circumstances did not warrant death." Id. at 695, 104 S.Ct. at 2069.

The Florida Supreme Court held that, even assuming deficient performance in counsel's failure to specifically ask Dr. Toomer whether either of the two statutory mental health mitigators applied, Hitchcock was not prejudiced "in light of the extensive mitigation that was presented [at resentencing] and the extremely weighty aggravators proven in this case." Hitchcock, 991 So.2d at 356-58. That conclusion is neither contrary to, nor an unreasonable application of, clearly established federal law. See 28 U.S.C. § 2254(d)(1). Counsel did have Dr. Toomer testify at the resentencing hearing that Hitchcock suffered from borderline personality disorder and that it would have affected him at the time of the crime by causing him to act impulsively. Based on Dr. Toomer's testimony, defense counsel argued in closing that Hitchcock was under the influence of extreme mental or emotional disturbance at the time of the offense, one of the statutory mitigating circumstances. The trial court found as non-statutory mitigating circumstances that Hitchcock was under the influence of lifelong personality difficulties at the time of the murder and that the murder was the result of an unplanned, impulsive act. There were four statutory aggravating circumstances, and Hitchcock was convicted of raping and murdering his brother's thirteen-year-old stepdaughter. Given those facts and circumstances, it was not unreasonable for the Florida Supreme Court to conclude there is no reasonable probability of a different result had counsel asked Dr. Toomer to state his ultimate opinion about whether the two statutory mitigating circumstances fit. We cannot say that no fairminded jurist could agree with that conclusion. See Holsey, 694 F.3d at 1257.

As to the second of Hitchcock's ineffective assistance claims, the Florida Supreme Court found that he had failed to establish either deficient performance or prejudice in regard to counsel's failure to have Hitchcock examined by a neuropsychologist for indications of brain damage. Hitchcock, 991 So.2d at 360. Because the Florida Supreme Court's finding of no prejudice was not unreasonable, we need not address the question of deficient performance. See Windom v. Sec'y, Dep't of Corr., 578 F.3d 1227, 1248 (11th Cir.2009) ("Because the failure to demonstrate either deficient performance or prejudice is dispositive ..., there is no reason for a court deciding an ineffective assistance claim to address both components of the inquiry if the defendant makes an insufficient showing on one.") (quotation marks and ellipsis omitted). We agree with the Florida Supreme Court, as well as the district court, that Hitchcock's evidence that he suffered from brain damage at the time of the murder was speculative at best and significantly undermined by the testimony that he was of normal intelligence, did not suffer from a major mental illness, and during the decades he had been in prison had not manifested behavior indicative of brain damage. Given the significant aggravating circumstances involved in his offense and found by the trial court, we cannot say that no fairminded jurist could agree with the Florida Supreme Court's determination that there is no reasonable likelihood of a lesser sentence had counsel obtained and presented the available evidence of brain damage.

III.

For these reasons, we affirm the district court's denial of Hitchcock's § 2254 petition for a writ of habeas corpus.

AFFIRMED.

WILSON, Circuit Judge, concurring in judgment:

With respect to Hitchcock's Eighth Amendment claim, I agree that the trial court did not violate clearly established federal law when it rejected this evidence as irrelevant to mitigation in these circumstances. However, I write separately to emphasize that under current Supreme Court precedent, contrary to the Majority's implication, such evidence is not per se irrelevant, and the Florida Supreme Court would not necessarily have erred had it found the evidence relevant under that precedent. Our holding today should not be taken to suggest that state courts may forego either a standard state-law relevance analysis or an analysis under Lockett simply because the evidence relates to plea negotiations. Further, the Majority's de novo review of the relevance of the evidence in this case is unnecessary to our holding.

Hitchcock's strongest argument is that the plea negotiations are relevant mitigation evidence because the fact that an offer was made implies that the prosecutor did not initially believe Hitchcock deserved to die, from which a jury could draw a variety of inferences about Hitchcock, the circumstances of his offense, and whether he deserves a penalty less than death. Hitchcock insists that the state cannot bar relevant mitigating evidence from being considered during the penalty phase as a matter of federal law. The Supreme Court has emphasized, including in precedent from this case, the need to admit relevant mitigating evidence into penalty proceedings in capital cases. See Lockett v. Ohio, 438 U.S. 586, 604, 98 S.Ct. 2954, 2964-65, 57 L.Ed.2d 973 (1978) (holding that the Eighth and Fourteenth Amendments "require that the sentencer, in all but the rarest kind of capital case, not be precluded from considering, as a mitigating factor, any aspect of a defendant's character or record and any of the circumstances of the offense that the defendant proffers as a basis for a sentence less than death" (emphasis omitted)); Eddings v. Oklahoma, 455 U.S. 104, 113-14, 102 S.Ct. 869, 876-77, 71 L.Ed.2d 1 (1982) (finding that the trial judge's refusal to consider evidence about the defendant's troubled childhood, particularly because he committed the crime at age sixteen, violated the rule articulated in Lockett because a sentencer cannot refuse to consider relevant mitigating evidence); Dugger, 481 U.S. at 399, 107 S.Ct. at 1824 (holding that failure to consider nonstatutory mitigating circumstances was reversible error because a sentencer cannot be precluded from considering relevant mitigating evidence). Indeed, the Supreme Court has demonstrated willingness to reverse a circuit court for unnecessarily limiting mitigation evidence in a capital case. See Tennard v. Dretke, 542 U.S. 274, 287, 124 S.Ct. 2562, 2571, 159 L.Ed.2d 384 (2004) (finding the Fifth Circuit's relevance test was too restrictive because "the question is simply whether the evidence is of such a character that it might serve as a basis for a sentence less than death" (citation omitted)).

The Supreme Court's emphasis on considering all relevant evidence as a matter of federal, constitutional law is an additional protection requiring states to be at least as generous in admitting mitigation evidence relating to a defendant's character, the record, and any of the circumstances of the offense as they would be in admitting mitigation evidence under their own rules. A rule that something is per se irrelevant — based in part on the fact that we have never deemed it relevant before — risks sending a signal to state courts that consideration of the evidence is prohibited.1 We clearly have no authority to make such a prohibition under state law, and we also lack that authority under federal law, as the rule is unsupported by Supreme Court precedent. Moreover, it turns the traditional concepts of relevance and admissibility on their heads by assuming that if we have not deemed a specific type of evidence relevant and admissible, it is not. The assumption should be that, as with any piece of evidence, the bar for relevance is low, and in mitigation in a capital sentence, it is lower still. See Lockett, 438 U.S. at 604, 98 S.Ct. at 2964 ("We are satisfied that this qualitative difference between death and other penalties calls for a greater degree of reliability when the death sentence is imposed.").

Therefore, while prior plea negotiations may not bear directly on a defendant's character, criminal record, or the circumstances of his offense, they may support inferences about one or more of those factors. Indeed, the Ninth Circuit held, in a capital case, that a "plea offer's mitigatory effect is clear: the prosecution thought this was not a clear-cut death penalty case." Scott v. Schriro, 567 F.3d 573, 584 (9th Cir.2009) (per curiam) (finding that evidence of a prosecutor's plea offer could be introduced during sentencing as mitigation).2 Further, even if the Majority is correct about the irrelevance of plea negotiations in this case, such negotiations may be relevant for a host of other reasons that should be evaluated as they arise.3 Contrary to the Majority's assertion, such evidence is not analogous either to evidence that, had a defendant's crime occurred a few hundred feet away, he would not have been charged with a capital offense, see United States v. Gabrion, 719 F.3d 511, 521 (6th Cir.2013) (en banc), or to evidence of the impact that a defendant's execution will have on his family members or friends, see United States v. Hager, 721 F.3d 167, 194-97 (4th Cir.2013). The former is merely a jurisdictional fact, and the latter does not relate to any party involved in the capital proceeding. By contrast, plea negotiations, at the very least, have the potential to be highly correlated to the nature of the crime or the defendant.

Further, the Majority's concern that allowing evidence of plea bargain offers at sentencing would discourage plea offers is outside the scope of our analysis. Given that a negotiated plea bargain saves a state from preparing for and trying a case entirely, it stretches logic to worry that prosecutors would stop offering plea bargains because, when such offers are denied, they may be admissible evidence in a subsequent sentencing. At worst, the evidence will cause the jury to recommend the very sentence that the prosecutor initially offered. In any event, it is unclear what authority permits us to factor such policy concerns into our evaluation of whether a piece of evidence is relevant.4 As the Majority concedes, it is not suggesting that the potentially "pernicious effect of discouraging prosecutors from extending plea offers" can justify excluding otherwise relevant mitigation evidence. Further, the Majority's insistence that a prior plea offer could simply reflect the desire to conserve prosecutorial resources or avoid the possibility of acquittal does not support its conclusion that such evidence is irrelevant. Instead, these are merely the points the government would likely offer to rebut a defendant's claim that the plea negotiations support an inference that the defendant deserves a sentence less than death. As with any evidence, the fact that competing inferences can be drawn does not render the evidence irrelevant.

Our decision is necessarily limited to whether or not the Florida Supreme Court's decision "was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court."5 28 U.S.C. § 2254(d)(1). We agree that it was not, and that conclusion alone resolves this case. Accordingly, I disagree with the Majority that this case calls for a "dual holding" regarding how this evidence would be treated under de novo review, and to the extent we decide this case on a de novo basis, we are adding dicta.

The Majority suggests that we have the authority to announce a dual holding — one under the applicable standard of review, and one under a clearly inapplicable standard of review. As a logical matter, it is of course true that "a habeas petitioner will not be entitled to a writ of habeas corpus if his or her claim is rejected on de novo review." Berghuis v. Thompkins, 560 U.S. 370, 390, 130 S.Ct. 2250, 2265, 176 L.Ed.2d 1098 (2010). This fact makes it more efficient and convenient in some cases to decide a case under both AEDPA's deferential standard and a de novo standard to avoid the potentially more difficult question of which standard of review is proper. In these cases, a dual holding makes it unnecessary to resolve an otherwise essential issue in the case. This was the situation in Knowles v. Mirzayance, where the Court articulated that habeas relief would be denied under either a de novo or deferential standard of review. 556 U.S. 111, 121 n. 2, 129 S.Ct. 1411, 1418 n. 2, 173 L.Ed.2d 251 (noting that the applicable standard of review was disputed); see also Berghuis, 560 U.S. at 390, 130 S.Ct. at 2265 ("[W]e need not determine whether AEDPA's deferential standard of review ... applies in this situation." (citation omitted)).

Where a dual holding does not obviate the need to answer an otherwise essential question to the case, however, the de novo aspect is entirely unnecessary to the resolution of the case, and is therefore by definition dicta. See Black's Law Dictionary (9th ed.2009) (defining "obiter dictum" as "[a] judicial comment made while delivering a judicial opinion, but one that is unnecessary to the decision in the case and therefore not precedential (although it may be considered persuasive)"). Here, there is no doubt that AEDPA's deferential standard of review resolves this case, so there is no need to resort to speculation about what we might do under a different standard of review. Hence, the invitation in Berghuis to "engag[e] in de novo review when it is unclear whether AEDPA deference applies." 560 U.S. at 390, 130 S.Ct. at 2265 (emphasis added). Further, the Supreme Court emphasizes the role of judicial restraint in deciding AEDPA cases. See, e.g., Tyler v. Cain, 533 U.S. 656, 668, 121 S.Ct. 2478, 2485, 150 L.Ed.2d 632 (2001) (stating that the Supreme Court "cannot" decide a question of retroactivity where, in light of AEDPA's statutory constraints on habeas review, the decision would not help the defendant and declining to address the question because any statement would be "dictum").6

Of course, even where it is clear that AEDPA deference applies, we may add dicta suggesting how we would decide the case were we to address it de novo. So, the fact that "we have employed this approach even when it was clear that the deference afforded by [AEDPA] applied," Reese v. Sec'y, Fla. Dep't of Corr., 675 F.3d 1277, 1291 (11th Cir.2012), should not be surprising. In doing so, however, we merely speculate on how we might decide future cases; we do not set precedent. To the extent Reese could be read to suggest that both aspects of a court's dual holding set binding precedent, that suggestion is itself dicta. In Reese, just as in this case, the only necessary holding was that "the Supreme Court of Florida did not unreasonably apply any clearly established federal rule when it rejected" the defendant's claim. Id. at 1287; see also id. at 1293-94 (Martin, J., concurring) ("This is not a case where it is unclear whether AEDPA deference applies.... Thus, de novo review is not called for by AEDPA, and it is not necessary for us to affirm...." (internal quotation marks omitted)).

Accordingly, the Majority's elaboration about how it would have treated this evidence were it to have de novo review is dicta, to which I would add that plea negotiations may be relevant under clearly established precedent in two ways — either if state rules deem them relevant or if, in a different situation, such evidence bears more clearly on a relevant mitigation factor. See, e.g., Guida, 549 F.3d at 403 (Merritt, J., dissenting).