
647 F.3d 535 (2011)
Marcus Ray Tyrone DRUERY, Petitioner-Appellant,
v.
Rick THALER, Director, Texas Department of Criminal Justice, Correctional Institutions Division, Respondent-Appellee.
No. 10-70022.
United States Court of Appeals, Fifth Circuit.
July 20, 2011.
*536 David A. Schulman (Court-Appointed), Law Office of David A. Schulman, Austin, TX, for Petitioner-Appellant.
*537 Leslie Katheryn Kuykendall, Asst. Atty. Gen., Postconviction Lit. Div., Austin, TX, for Respondent-Appellee.
Before JONES, Chief Judge, and JOLLY and SOUTHWICK, Circuit Judges.
EDITH H. JONES, Chief Judge:
Petitioner Marcus Ray Tyrone Druery ("Petitioner") was convicted of capital murder and sentenced to death by a Texas court. After failing to obtain relief in state court or the United States Supreme Court, Petitioner sought a federal habeas petition, which the district court denied. The district court also denied Petitioner a certificate of appealability ("COA"). Petitioner now asks this court to grant him a COA pursuant to 28 U.S.C. § 2253. After reviewing the record and the parties' briefing, we conclude that the motion should be DENIED.

I. Background

Statement of the Case
Petitioner was convicted of capital murder after a jury trial and sentenced to death by lethal injection. Petitioner's conviction and sentence were affirmed by the Texas Court of Criminal Appeals, Druery v. State, 225 S.W.3d 491 (Tex.Crim.App. 2007), cert. denied, 552 U.S. 1028, 128 S.Ct. 627, 169 L.Ed.2d 404 (2007), after which Petitioner sought state habeas relief. After failing to obtain relief in the state courts, Ex parte Druery, 2008 WL 748479 (Tex.Crim.App. Mar.19, 2008), Petitioner filed for federal habeas relief, which the district court denied on July 26, 2010. Druery v. Thaler, 2010 WL 2991066 (S.D.Tex. July 26, 2010). The district court also held that Petitioner was not entitled to a COA. Id. at *12. Petitioner now appeals, requesting a COA from this court.

Factual Background
Since the key facts of this case are presented in the district court opinion, Druery v. Thaler, supra, only a brief summary is required here.
Petitioner was convicted of murdering Skyyler Browne, a fellow student at Texas State Technical College in Waco, Texas. Before the murder, Petitioner had asked Browne to travel with him to Bryan, Texas. Although Browne initially hesitated, he eventually agreed to go. After an evening of partying in Bryan, Petitioner, Browne, and two other individuals drove to a stock pond on a rural property owned by Petitioner's family. While Browne was standing near the pond, Petitioner held a gun within six inches of Browne's head and fired. As Browne's body fell, Petitioner fired a second shot into Browne's neck, and then a third shot as Browne lay on the ground. Petitioner returned to the vehicle in which the group arrived, carrying with him Browne's cell phone, money, marijuana, and gun. Joquisha Pitts, who was present that evening, later informed the police about the murder.
After trial, the jury found Petitioner guilty of capital murder for killing Browne during the course of robbing or attempting to rob him. During the penalty phase, the jury found beyond a reasonable doubt that there is a probability that Petitioner would commit criminal acts of violence that would constitute a continuing threat to society. The jury also found that the mitigating evidence presented by defense counsel was insufficient to merit a life sentence. Accordingly, the trial court sentenced Petitioner to death.


*538 II. Standard for Certificate of Appealability
Under AEDPA, 28 U.S.C. § 2253(c)(2), a convict seeking a COA must make "a substantial showing of the denial of a constitutional right." In Miller-El v. Cockrell, 537 U.S. 322, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003), the U.S. Supreme Court clarified: "A petitioner satisfies this standard by demonstrating that jurists of reason could disagree with the district court's resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further." Id. at 327, 123 S.Ct. at 1034 (citing Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000)). Importantly, in determining this issue, we "view[] the petitioner's arguments through the lens of the deferential scheme laid out in 28 U.S.C. § 2254(d)." Barrientes v. Johnson, 221 F.3d 741, 772 (5th Cir.2000). Under § 2254(d), when reviewing a claim adjudicated by a state court on the merits, we defer to the state court's decision regarding that claim, unless the decision "[is] contrary to, or involve[s] an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or . . . [is] based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." Id. (quoting 28 U.S.C. § 2254(d)(1) & (2)).

III. Discussion
Petitioner raises five claims on appeal of the district court's decision to deny him a certificate of appealability ("COA"). First, Petitioner raises an ineffective assistance of counsel claim because trial counsel declined a jury instruction on the lesser-included offense of murder. Second, Petitioner asserts ineffective assistance of counsel based on trial counsel's failure to investigate and plan a mitigation defense for the punishment phase. Third, Petitioner asserts that the penalty phase jury charge denied his due process rights and violated the Eighth Amendment because it did not inform the jury that Petitioner would automatically receive a life sentence if the jurors did not reach a unanimous verdict on one or both of the special issues. Fourth, the trial court deprived Petitioner of due process by not sua sponte instructing the jury on the lesser-included offense of murder. Fifth, the trial court violated Petitioner's Sixth and Fourteenth Amendment rights by not instructing the jury that the State bore the burden of proof to negate Petitioner's mitigation evidence.

A. INEFFECTIVE ASSISTANCE OF COUNSEL.
We review these claims of ineffective assistance of counsel under the familiar standard of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
In order to prevail on his ineffective assistance claims, Petitioner must demonstrate that (1) counsel's representation fell below an objective standard of reasonableness and that (2) there is a reasonable probability that prejudice resulted. See Bower v. Quarterman, 497 F.3d 459, 466 (5th Cir.2007) (citing Strickland, 466 U.S. at 694, 104 S.Ct. 2052, 80 L.Ed.2d 674). Strickland itself calls for considerable deference in evaluating the reasonableness of the attorney's conduct. See Cullen v. Pinholster, ___ U.S. ___, 131 S.Ct. 1388, 1403, 179 L.Ed.2d 557 (2011) (counsel should be "strongly presumed to have rendered adequate assistance and made all significant decisions in the exercise of reasonable professional judgment" (quoting Strickland, 466 U.S. at 690, 104 S.Ct. 2052, 80 L.Ed.2d 674)). When our review is governed by AEDPAas is the case *539 hereour review of the state court's resolution of the ineffective-assistance-of-counsel claim is "doubly deferential", id. (quoting Knowles v. Mirzayance, 556 U.S. ___, 129 S.Ct. 1411, 1413, 173 L.Ed.2d 251 (2009)), since the question is "whether the state court's application of the Strickland standard was unreasonable." Harrington v. Richter, ___ U.S. ___, 131 S.Ct. 770, 785, 178 L.Ed.2d 624 (2011). Importantly, "[t]his is different from asking whether defense counsel's performance fell below Strickland's standard," because the "state court must be granted a deference and latitude that are not in operation when the case involves review under the Strickland standard itself." Id. Consequently, "even a strong case for relief does not mean the state court's contrary conclusion was unreasonable." Id. at 786. Rather, in order to obtain habeas relief, "a state prisoner must show that the state court's ruling on the claim being presented in federal court was so lacking in justification that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement." Id. at 786-87.
In addition to this cumulation of deferential standards, we also recall the precise standard for a COA. Petitioner must demonstrate that "reasonable jurists could debate" whether the petition should have been resolved by the district court in a different manner or "that the issues presented were adequate to deserve encouragement to proceed further." Barrientes, 221 F.3d at 772. With these standards in mind, we address each ineffective assistance claim in turn.

1. Counsel's Failure To Request Instruction On Lesser-Included Offense of Murder.
Under Texas law, a person is guilty of capital murder if he commits murder as defined by Section 19.02(b)(1) and he intentionally does so "in the course of committing or attempting to commit . . . robbery." TEX. PENAL CODE § 19.03(a)(2). Petitioner contends that his trial counsel, Craig Washington ("Washington"), was ineffective because he refused to agree to a lesser-included offense instruction for first-degree murder.
In this case, the state habeas court found that Washington's punishment theory of the case was that Druery did not intend to steal Browne's property at the time Petitioner killed Browne and, thus, Petitioner was not guilty of capital murder. The court relied, in part, upon Washington's sworn affidavit and hearing testimony expressing his conviction that the State would not be able to prove the aggravating element of robbery. Washington believed that if the jury "only had a choice of capital murder, then they would have no choice but to acquit him." For this reason, Washington "specifically declined the opportunity to request a jury charge instruction on the lesser included offense of murder."
Petitioner "admits that it was trial counsel's `strategy' to reject the lesser included instruction." Petitioner argues, however, that the strategy was based on a misunderstanding of the law, and thus cannot have been reasonable. Washington testified that at the time he made the decision to decline the jury charge, he believed that another jury could try Petitioner for murder at a later time. Washington was mistaken, since the Double Jeopardy Clause would have barred retrial following an acquittal of capital murder. See Brown v. Ohio, 432 U.S. 161, 169, 97 S.Ct. 2221, 2227, 53 L.Ed.2d 187 (1977) ("[T]he Fifth Amendment forbids successive prosecution. . . for a . . . lesser included offense."). Petitioner contends that Washington was *540 ineffective because his strategy rested upon on an incorrect "belief that he could argue to the jury that [Petitioner] could be tried again on a murder charge if acquitted of capital murder."
The state habeas court found, however, that Washington articulated a valid strategic reason for declining the instruction: to obtain a full acquittal. Washington believed that the State introduced evidence sufficient to prove murder but not the aggravating circumstance of robbery. In light of the state habeas court's additional finding that Petitioner and his family rejected the State's offer of a life sentence, this all-or-nothing strategy was not objectively unreasonable. Strickland directs courts to consider the conduct of defense counsel based on the objective standard of the reasonable attorney. See 466 U.S. at 688, 104 S.Ct. at 2065. That Washington may have been mistaken in part of his legal reasoning does not constitute ineffectiveness where the ultimate strategic choice was reasonable. Consequently, it is not debatable that the state court's resolution of this issue was not unreasonable.

2. Failing To Investigate And Plan Mitigating Evidence.
The second ineffective assistance claim relates to Washington's alleged failure to investigate potentially mitigating evidence or prepare a mitigation defense at the punishment phase of trial. Petitioner asserts that Washington did not begin to prepare his mitigation case until after the jury convicted Petitioner of capital murder, and he never hired a mitigation specialist or psychological expert. Petitioner also attempts to show prejudice by arguing that an investigation would have uncovered evidence of possible brain damage.
In reviewing this claim, the state habeas court credited Washington's assertion that Petitioner's family hired an investigator who worked under Washington's direction and helped Washington prepare for both phases of trial. The court also found that Washington in fact formulated a theory for the penalty phase of trialthat Petitioner's "violent behavior was due to drug use, and that he would not be a danger to anyone while in the structured environment of prison." Testimony adduced at trial supports this strategy, as even Petitioner appears to acknowledge. See Pet'r's Br. at 23-24 (Washington presented his theory"that [Petitioner] was a good person when he was not on drugs and he would not be on drugs in prison" "through lay witnesses"). For example, a number of witnesses testified that Petitioner was a fine person as a young man. Other testimony, working in tandem with the former, communicated that Petitioner was different when he was on drugs. Petitioner's grandmother testified that Petitioner's behavior changed and that she suspected him of drug use. Other witnesses testified about particular violent or reckless acts during which they perceived Petitioner as being "on something," or "under the influence of drugs." Petitioner's former girlfriend affirmed that "[Petitioner] was always acting crazy when he was on drugs." In light of this and other testimony, the court concluded that defense counsel "prepared and presented a thorough punishment case consistent with their theory."
Petitioner also alleges that Washington failed to hire a mitigation specialist or psychologist, and to investigate potential physical or mental problems that may have affected Petitioner's behavior. While there is some evidence Washington turned over records to a psychologist, Dr. *541 Windell, Dickerson,[1] and that Washington suggested to the family that Petitioner be subjected to a mental health examination, the record is largely bereft of evidence of any serious inquiry into Petitioner's mental health. According to Washington, no mental health professional ever examined Petitioner because Petitioner's family rejected the suggestion. Even if we assumed, arguendo, this conduct fell below an objective standard of reasonableness,[2] two findings of the state court support its ultimate holding.
First, this court has held that "[a] defendant who alleges a failure to investigate on the part of his counsel must allege with specificity what the investigation would have revealed and how it would have altered the outcome of the trial." Nelson v. Hargett, 989 F.2d 847, 850 (5th Cir.1993) (quoting United States v. Green, 882 F.2d 999, 1003 (5th Cir.1989)). In this case, Petitioner did offer some evidence suggesting that Petitioner may have sustained brain damage as a result of drug use. Pet'r's Br. at 26 (citing Bette Burke's affidavit), 28 (quoting Dr. Rustin's report and affidavit). However, the state court found that Bette Burke's affidavit contained mere conclusions and speculation, and was thus not credible. Moreover, Dr. Rustin admitted that he was not qualified to ascertain whether Petitioner had experienced brain damage because of drug use, especially since doing so would have required testing prior to drug use. Dr. Rustin also testified that in his opinion, Petitioner was intoxicated at the time of the murder, and this was not a result of long-term chronic brain damage. Thus, the state court was not unreasonable in concluding that Petitioner failed to present credible evidence of actual brain injury, disease, or physical/mental defect. Petitioner has failed to prove that an investigation would have yielded mitigation evidence.
Second, even if Washington did unreasonably fail to investigate areas of Petitioner's mental health and such investigation would have yielded useful information, the state court also noted that such evidence could have undermined defense counsel's theory. As the state court found, "[p]resentation of some type of brain injury could indicate that [Petitioner]'s violent behavior was of a permanent nature not induced by drug use, suggesting he could be a future threat to those in prison." Such evidence, according to the court, would be "double-edged mitigation evidence," since it could undermine Washington's *542 theory that once separated from drugs, Petitioner would no longer be a continuing threat to those in prison. Or, as the State argued, "expert testimony suggesting that [Petitioner]'s condition was permanent would have eviscerated counsel's defensive theory."
Consequently, we agree with the district court that the state court's resolution of this issue is not debatable among reasonable jurists.

B. TEXAS'S "12-10" JURY INSTRUCTION.
Petitioner next challenges Texas's "12-10" rule jury instructions as unconstitutional under the Sixth, Eighth, and Fourteenth Amendments. Under Texas law, the jury must consider two special issues before the death penalty is imposed on a capital defendant. First, the trial court is required to submit the following "aggravating" special issue to the jury: "whether there is a probability that the defendant would commit criminal acts of violence that would constitute a continuing threat to society." TEX.CODE CRIM. PROC. ANN. art. 37.071(2)(b)(1). If the jury unanimously answers "yes," the jury must then answer the following "mitigation" issue: "[w]hether, taking into consideration all of the evidence, including the circumstances of the offense, the defendant's character and background, and the personal moral culpability of the defendant, there is a sufficient mitigating circumstance or circumstances to warrant that a sentence of life imprisonment without parole rather than a death sentence be imposed." Id. art. 37.071(2)(e)(1). If the jury unanimously answers "no," then the defendant is sentenced to death. Id. art. 37.071(2)(g).
Pursuant to these provisions, the trial court was also required to instruct the jury that it must have at least 10 "no" votes to answer "no" on the aggravating special issue, and at least 10 "yes" votes to answer "yes" on the mitigation special issueeither of which answers would result in a life sentence, not death. Id. art. 37.071(2)(g). Petitioner argues that this so-called "12-10" instruction misleadingly implied that the jury could not return a life sentence unless at least 10 jurors agreed on an answer to one of the special issues. (In reality, the trial court is required to impose a life sentence if the jury is unable to answer either special issue. Id. art. 37.071(2)(g).[3]) According to the Petitioner, this was a he which operated to relieve jurors of their individual responsibilities in the process, which denied Petitioner's right to due process, "to a fair and impartial jury" under the Sixth Amendment, and to freedom from cruel and unusual punishment under the Eighth Amendment.
To the extent Petitioner's challenge to Texas's 12-10 rule rests on Mills v. Maryland, 486 U.S. 367, 108 S.Ct. 1860, 100 L.Ed.2d 384 (1988) and the Eighth Amendment, as well as due process under the Fourteenth Amendment, it is foreclosed by Fifth Circuit precedent. In Mills, the Supreme Court held that a capital sentencing scheme violated the Eighth Amendment by precluding the jury from considering mitigating evidence unless the jury unanimously agreed that a particular circumstance was supported by the evidence. Id. The Fifth Circuit has refused, however, to *543 invalidate the Texas sentencing scheme based on this decision.
In Miller v. Johnson, this court rejected an Eighth Amendment challenge to Texas's 12-10 rule, despite Petitioner's argument that it created the risk that (1) one or more jurors would change a vote to satisfy the majority, and that (2) a reasonable juror would believe that his individual vote was not meaningful unless some threshold number of jurors were in agreement on that particular special issue. 200 F.3d 274, 288 (5th Cir.2000). The court stated that "Mills is not applicable to the capital sentencing scheme in Texas." Id. More recently, this court rejected a petitioner's claim that Texas's 12-10 Rule violated due process and the right to freedom from cruel and unusual punishment. Hughes v. Dretke, 412 F.3d 582, 593-94 (5th Cir.2005). The court held that Teague barred it from extending Mills to invalidate the Texas scheme. Id. at 594. And since "no clearly established federal law call[ed] into doubt the Texas death penalty statute," the court declined to issue a COA on this claim. Id.[4] While one Seventh Circuit case arguably supports Petitioner's claims under the Eighth and Fourteenth Amendments, Kubat v. Thieret, 867 F.2d 351, 372-74 (7th Cir.1989) (finding that the court's failure to expressly inform jurors that if even one juror believed that the death penalty should not be imposed, the petitioner would not be sentenced to death, ran afoul of Mills), this case does not supercede intervening Fifth Circuit precedent regarding challenges to Texas' 12-10 rule.[5]
Petitioner also relies upon Caldwell v. Mississippi, 472 U.S. 320, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985), for his Eighth Amendment claim. In Caldwell, the Supreme Court held that "it is constitutionally impermissible to rest a death sentence on a determination made by a sentencer who has been led to believe that the responsibility for determining the appropriateness of the defendant's death rests elsewhere." Id. at 328-29, 105 S.Ct. at 2639. In Dugger v. Adams, 489 U.S. 401, 109 S.Ct. 1211, 103 L.Ed.2d 435 (1989), the Supreme Court clarified its holding in Caldwell, stating that to "establish a Caldwell violation, a defendant necessarily must show that the remarks to the jury improperly described the role assigned to the jury by local law." Id. at 407, 109 S.Ct. at 1215; see also Montoya v. Scott, 65 F.3d 405, 420 (5th Cir.1995) (discussing Caldwell and Dugger). In this case, Petitioner argues that the challenged instructions embody an "inherent lie" since Texas *544 law forbids jurors from being told the consequence of their failure to answer the special issues. According to Petitioner, this has an "effect" on the individual jurorsnamely, it "denies the individual juror's responsibilities, and diminishes the individual juror's understanding, and acceptance, of that individual responsibility." Since jurors may allegedly interpret the jury instructions as relieving them of their responsibility, Petitioner asserts that Caldwell is violated unless each juror is informed as to the individual importance of his vote.
Petitioner acknowledges that at first glance, Jones v. United States, 527 U.S. 373, 381, 119 S.Ct. 2090, 2098, 144 L.Ed.2d 370 (1999)which held that "the Eighth Amendment does not require that the jurors be instructed as to the consequences of their failure to agree"appears to be dispositive. He argues, however, that while a court might not be constitutionally compelled to inform the jury of the consequences of their inability to reach a verdict, it is impermissible to lie to the jury regarding "their constitutional and statutory responsibilities and their individual abilities to resolve the punishment issue." The lone hold-out juror may capitulate to the majority under a mistaken belief that the 12-10 Rule requires him to do so. Moreover, Petitioner suggests that the failure to explain to the jury important elements of the sentencing scheme creates an intolerable risk of confusing the jury.
Caldwell does not, however, clearly support Petitioner's argument. In that case, the prosecution urged the jury not to view itself as finally determining whether petitioner would die, because a death sentence would be reviewed for correctness by the state supreme court. Caldwell, 472 U.S. at 323, 105 S.Ct. at 2636. The Court held that this violated the Eighth Amendment since it led jurors to believe that "the responsibility for determining the appropriateness of the defendant's death rest[ed] elsewhere." Id. at 328-29, 105 S.Ct. at 2639.
In this case, Druery does not explain how the jurors would believe that the responsibility to determine the propriety of a death sentence rested elsewhere. The 12-10 Rules implicitly urge jurors toward consensus, but nothing in them suggests the ultimate responsibility to choose reposes in another actor. Moreover, while jurors were admittedly not told what would result from their failure to agree on a special issue, Petitioner fails to show that the jury instructions misstated their role under local law. Cf. Dugger, 489 U.S. at 407, 109 S.Ct. at 1215.
Petitioner also asserts that the 12-10 Rules violates his Sixth Amendment rights. It is unclear what cases he uses to support this claim, or how this is an argument distinct from the others discussed above.
Finally, Petitioner asserts that the 12-10 Rules violates his due process rights as well. Petitioner cites the Supreme Court decision in Kelly v. South Carolina, 534 U.S. 246, 122 S.Ct. 726, 151 L.Ed.2d 670 (2002), for the proposition that the trial court has a duty "to give instructions sufficient to explain the law," and that the instructions must be sufficiently clear. Id. at 256, 122 S.Ct. at 733. In Kelly, the Supreme Court held that due process entitled a capital defendant to a jury instruction that he would be ineligible for parole under a life sentence. Id. Parol eligibility, of course, is not an issue raised in this petition. Rather, the question is whether the jury must be instructed as to the consequence of their failure to agree on the special issues regarding aggravating and mitigating factors. Adopting Petitioner's argument would require an extension of Kelly, which is impermissible on habeas *545 review. See Teague v. Lane, 489 U.S. 288, 310, 109 S.Ct. 1060, 1075, 103 L.Ed.2d 334 (1989).
Petitioner has not demonstrated that he is entitled to a COA on this issue.

C. TRIAL COURT'S FAILURE TO SUA SPONTE INSTRUCT JURY ON LESSER-INCLUDED OFFENSE OF MURDER.
Petitioner next argues that the trial court erred "by not sua sponte instructing the jury on first-degree murder." While Petitioner admits that trial counsel "rejected the lesser included instruction," Petitioner argues instead that he only did so because of a misunderstanding of the law. Thus, according to Petitioner, the trial court had a constitutional duty to correct, sua sponte, counsel's error at trial. As Petitioner states, "[T]he trial court should have overruled Mr. Washington's ill-informed decision [to decline the jury charge] and instructed the jury on the lesser included offense of murder." Notably, Petitioner cites no case law for the proposition that trial courts have a duty to overrule such a decision made by trial counsel.
On direct review, the Texas Court of Criminal Appeals declined to review this claim because the court found the invited-error doctrine estopped him from raising it. Druery v. State, 225 S.W.3d 491, 505-06 (Tex.Crim.App.2007), cert. denied, 552 U.S. 1028, 128 S.Ct. 627, 169 L.Ed.2d 404 (2007). The court reasoned that "Druery not only did not object to the omission of the lesser-included instruction on first-degree murder but . . . he affirmatively requested. . . that the lesser-included instruction not be given." Id. at 506. As a result, he was barred from raising a claim of error on appeal. Id.
To support his position, Petitioner cites two Supreme Court decisions holding that "due process requires that a lesser included offense instruction be given when the evidence warrants such an instruction." Hopper v. Evans, 456 U.S. 605, 611, 102 S.Ct. 2049, 2053, 72 L.Ed.2d 367 (1982) (citing Beck v. Alabama, 447 U.S. 625, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980)). But even if Petitioner was entitled to such an instruction under Beck, Petitioner's decision to decline the lesser-included instruction bars him from raising it now.
The invited-error doctrine provides that "a defendant cannot complain on appeal of alleged errors which he invited or induced, especially where the defendant may not have been prejudiced by the error." United States v. Green, 272 F.3d 748, 754 (5th Cir.2001) (citing United States v. Raymer, 876 F.2d 383, 388 (5th Cir.1989)). This doctrine applies to habeas review as well. See, e.g., Fields v. Bagley, 275 F.3d 478, 486 (6th Cir.2001) ("When a Petitioner invites an error in the trial court, he is precluded from seeking habeas corpus relief for that error."); Parker v. Champion, 148 F.3d 1219, 1221-22 (10th Cir.1998) (noting that habeas relief on the basis of an invited error is precluded); Wilson v. Lindler, 8 F.3d 173, 175 (4th Cir.1993) (en banc) ("Even if we were to find such error in the trial of this case in the state court, the error was invited and therefore cannot form the basis for habeas corpus relief."). In this case, Petitioner admits that his attorney "rejected the lesser included instruction." Moreover, the Texas Court of Criminal Appeals explicitly refused to consider the merits of Petitioner's claim based on the invited-error doctrine. Druery, 225 S.W.3d at 506.
The invited-error doctrine qualifies as a state procedural bar. See, e.g., Leavitt v. Arave, 383 F.3d 809, 832-33 (9th Cir.2004) (suggesting that the invited error rule is a state procedural bar); Tucker v. *546 Johnson, 115 F.3d 276, 281 (5th Cir.1997) (holding that petitioner could not overcome procedural default of invited-error doctrine); Coleman v. O'Leary, 845 F.2d 696, 699 (7th Cir.1988) (referring to invited error as a "state procedural rule"). Petitioner may overcome this bar only by showing "cause for the default and actual prejudice as a result of the alleged violation of federal law" or "that failure to consider the claims will result in a fundamental miscarriage of justice." Neville v. Dretke, 423 F.3d 474, 480 (5th Cir.2005) (quoting Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 2565, 115 L.Ed.2d 640 (1991)).
Petitioner's principal argument on this issue centers on his trial counsel's alleged deficient performance. However, since Petitioner has not made a showing that counsel was ineffective in refusing the instruction, he has not shown cause. Cf. Tucker, 115 F.3d at 281 (applying pre-AEDPA standards, but finding ineffective assistance of counsel not to be sufficient cause to overcome bar of invited-error doctrine where petitioner failed to show counsel was ineffective). Accordingly, Petitioner has not demonstrated that he is entitled to a COA on this issue.

D. FAILURE TO PROVIDE BURDEN OF PROOF ON MITIGATION SPECIAL ISSUE.
Finally, Druery contends that he was denied a fair trial and "due process when the trial court failed to instruct the jury that the State bore the burden of proof to negate [Petitioner]'s mitigation evidence." According to Petitioner, the trial court's "failure to place the burden of proof on the State unconstitutionally placed on [Petitioner] the burden to produce mitigating evidence sufficient to convince the jury a life sentence, rather than a death sentence, should be imposed." "Under such circumstances. . . a jury cannot determine how it is to weigh the competing forms of evidence to arrive at a verdict worthy of reliability."
In order to obtain a death sentence under Texas law, the State has the burden to prove beyond a reasonable doubt that "there is a probability that the defendant would commit criminal acts of violence that would constitute a continuing threat to society." TEX.CODE CRIM. PROC. ANN. art. 37.071(2)(b)(1). If the jury finds future dangerousness, the jury must then consider whether there are sufficient mitigating circumstances to warrant a sentence of life imprisonment rather than a death sentence. Id. art. 37.071(2)(e)(1). While the jury may not answer the latter issue "no" unless they unanimously agree, id. art. 37.071(2)(f), the sentencing scheme does not assign a burden of proof on this issue. This, Petitioner contends, violates his constitutional rights to due process and a fair trial, since the State is not required to negate Petitioner's mitigation evidence.
This court has held that "[n]o Supreme Court or Circuit precedent constitutionally requires that Texas's mitigation special issue be assigned a burden of proof." Rowell v. Dretke, 398 F.3d 370, 378 (5th Cir.2005). In Avila v. Quarterman, this court rejected a petitioner's argument "that allowing a sentence of death without a jury finding beyond a reasonable doubt that there were no mitigating circumstances sufficient to warrant a sentence of life imprisonment violated his Sixth and Fourteenth Amendment right to due process and a fair trial." 560 F.3d 299, 315 (5th Cir.2009). Other decisions have likewise rejected the argument that failure to instruct the jury that the State has the burden of proof beyond a reasonable doubt on the mitigation issue is unconstitutional. See, e.g., Scheanette v. Quarterman, 482 F.3d 815, 828 (5th Cir.2007); Granados v. Quarterman, 455 F.3d 529, 536-37 (5th *547 Cir.2006); see also Pet'r's Br. at 60 ("[Petitioner] concedes that the case law is against him."). Consequently, this argument by Petitioner is foreclosed by Fifth Circuit precedent and not subject to debate among jurists.

IV. Conclusion
For the reasons stated above, Petitioner's request for a COA is DENIED.
NOTES
[1]  The state habeas court found that Washington turned over records to Dr. Windell Dickerson, a psychologist, in order for Dr. Dickerson to determine whether a body of information was available that could have been used for mitigation. According to Washington, he gave to Dr. Dickerson "the information that was available about [Petitioner] concerning some things that he had done in the recent past" and "the medical records that had been made available" by the prosecutor, Mr. Turner.
[2]  Petitioner relies upon ABA Guidelines and State Bar of Texas Guidelines to support his ineffective-assistance-of-counsel claim. We note that while these may be "useful as `guides' to what reasonableness entails," they certainly do not define reasonableness. Bobby v. Van Hook, ___ U.S. ___, 130 S.Ct. 13, 16, 175 L.Ed.2d 255 (2009) (per curiam). Best practices urged by the ABA do not necessarily track the contours of the Sixth Amendment. Consequently, the guidelines do not function as "inexorable commands" with which all capital defense counsel "must fully comply." See id. at 17. In addition, even when we do consider them, they are useful only to the extent "they describe the professional norms prevailing when the representation took place." Id. at 16. In this case, the probative value of the Texas guidelines is diminished by the fact that they were adopted by the State Bar of Texas nearly three years after Petitioner's trial.
[3]  This provision states: "If the jury returns a negative finding on any issue submitted under Subsection (b) or an affirmative finding on an issue submitted under Subsection (e)(1) or is unable to answer any issue submitted under Subsection (b) or (e), the court shall sentence the defendant to confinement in the Texas Department of Criminal Justice for life imprisonment without parole." (emphasis added)
[4]  See also Alexander v. Johnson, 211 F.3d 895, 897 n. 5 (5th Cir.2000) ("In addition to . . . being barred by Teague, [Petitioner]'s substantive argument is meritless. The Supreme Court recently rejected the theory that a district court's failure to instruct the jury as to the consequences of deadlock gives rise to an Eighth Amendment violation. Furthermore, the Fifth Circuit has expressly rejected the contention that Texas's 10-12 Rule prevents jurors from considering mitigating circumstances." (internal citations omitted)); Woods v. Johnson, 75 F.3d 1017, 1036 (5th Cir.1996) (claim that "the instruction that the jury could not answer any punishment special issue `no' unless at least ten jurors concurred in that answer violated the rule of Mills" lacks "substantive merit" since "the instruction at issue is wholly dissimilar to that involved in Mills"); Webb v. Collins, 2 F.3d 93, 96 (5th Cir.1993) (finding challenge to Texas's capital sentencing scheme under Mills barred by Teague).
[5]  Jacobs v. Scott also rejected a challenge to the 12-10 rule. 31 F.3d 1319, 1328 (5th Cir. 1994). While the relevant Texas statute at the time did not include the instruction on the mitigation special issue, the court reasoned that unlike in Mills, the Texas system here still allowed each juror to take into account any mitigating circumstances, and thus did not permit a single juror to preclude the entire jury from considering them. Id. at 1329.
