Penry filed a motion for a certificate of appealability (COA) in this § 2254 capital habeas proceeding alleging various constitutional violations. For the reasons that follow, we deny his motion.
I
Penry was convicted of capital murder and sentenced to death in Texas state court for the rape and murder of Pamela Carpenter. Penry raped Carpenter and stabbed her with a pair of scissors. He had met her several weeks earlier while helping to install appliances in her home. Penry matched the description Carpenter gave of her attacker before she died. After being given his Miranda warnings, Penry gave an oral confession and later a signed confession to the rape and murder. At trial, Penry offered mitigating evidence that he was mentally retarded and abused *507as a child. He was convicted and sentenced to death. The United States Supreme Court granted federal habeas relief and vacated his sentence, holding that Penry’s rights were violated by jury instructions the trial court gave at the punishment phase of his trial.1 The court found that none of the three special statutory questions provided to the jury, under Texas law, allowed the jury to give effect to Penry’s mitigating evidence. “The jury was never instructed that it could consider the evidence offered by Penry as mitigating evidence and that it could give mitigating effect to that evidence.”2
In the second trial, the trial court followed the Texas statutory scheme and gave the jury the same three special questions it had given the jury in the first trial. However, the judge also provided supplemental instructions directing the jury to consider any other relevant mitigating evidence and explained how to give effect to that evidence. Penry was again convicted of capital murder and sentenced to death. The sentence was again affirmed on direct appeal3 and state habeas relief was denied. The district court also denied Pen-ry’s application for a COA. Penry now seeks a COA from this court. We granted Penry’s motion for a stay of execution in order to consider his motion for a COA.
II
A COA may only issue if the petitioner makes a “substantial showing of the denial of a constitutional right.”4 This burden can be met if the issues presented “are debatable among jurists of reason; ... a court could resolve the issues in a different manner; or .. .the questions are adequate to deserve encouragement to proceed further.”5
A death sentence alone does not justify the automatic issuance of a COA, although it is a proper consideration.6 Any doubts as to whether the COA should issue are to be resolved in the petitioner’s favor.7
Penry’s petition was filed after the enactment of the Antiterrorism and Effective Death Penalty Act (AEDPA). Thus, for questions of law or mixed questions of law and fact adjudicated on the merits in state court, we may grant federal habeas relief under 28 U.S.C. § 2254(d)(1) only if the state court decision “was contrary to, or involved an unreasonable application of, clearly established [Supreme Court precedent].”8 A state court decision is “contrary to” Supreme Court precedent if: (1) the state court’s conclusion is “opposite to that reached by [the Supreme Court] on a question of law” or (2) the “state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent” and arrives at an opposite result.9 A state court unreasonably applies Supreme Court precedent if: (1) it unreasonably applies the correct legal rule to the facts of a particular case or *508(2) it “unreasonably extends a legal principle from [Supreme Court] precedent to a new context where it should not apply or unreasonably refuses to extend that principle to a new context where it should apply.”10 In deciding whether a state court’s application was unreasonable, this court considers whether the application was “objectively unreasonable.”11 We now turn to Penry’s specific arguments on appeal.
Ill
Penry first argues that the jury instructions given during the punishment phase of his trial did not allow the jury to consider and give effect to mitigating evidence regarding his alleged mental retardation and severe child abuse; thus, the instructions violated the Supreme Court’s directive in Penry v. Lynaugh12 {“Penry I ”). Penry explains that jurors could only give effect to his mitigating evidence, as the Supreme Court required in Penry I, and grant him a life sentence if they found that the evidence fit under one of the three special questions required by Texas law.13 In Penry I, Penry’s federal habeas challenge to his first trial and conviction, the Supreme Court found that, under the trial court’s instruction, none of the three special statutory questions allowed the jury to give effect to Penry’s mitigating evidence. At Penry’s retrial, however, the trial court supplemented the instruction it gave in Penry I. The court instructed the jury to consider any mitigating circumstances supported by the evidence. The instruction stated, in part:
[W]hen you deliberate on the questions posed in the special issues, you are to consider mitigating circumstances, if any, supported by the evidence.... A mitigating circumstance may include, but is not limited to, any aspect of the defendant’s character and record or circumstances of the crime which you believe could make a death sentence inappropriate in this case. If you find ... any mitigating circumstances ... you must decide how much weight they deserve, if any, and ... give effect and consideration to them in assessing the defendant’s personal culpability at the time you answer the special issue. If you determine, when giving effect to the mitigating evidence, if any, that a life sentence, as reflected by a negative finding to the issue under consideration, rather than a death sentence, is an appropriate response to the personal culpability of the defendant, a negative finding should be given to one of the special issues.
Penry correctly contends that the instruction still required the jury to give a negative answer to one of the three special issues in order for Penry to receive a life sentence. Penry argues that because childhood abuse and mental retardation do not necessarily fit within the scope of any of the special issues, this instruction did not allow the jury to give effect to these mitigating circumstances. However, on direct appeal, the Texas Court of Criminal Appeals found that the instruction satisfied the requirements of Penry I and allowed the jury to give effect to those mitigating circumstances.14
We agree with the district court that the Texas Court of Criminal Appeals’s holding *509that the challenged instruction was constitutional was not an unreasonable application of clearly established law, namely Penry I. The instruction directed the jury to consider and give effect to any mitigating circumstances supported by the evidence by answering “no” to one of the special issues if they felt a life sentence was appropriate. This instruction satisfied the deficiency in the trial court’s instruction identified in Penry I: “[t]he jury was never instructed that it could consider the evidence offered by Penry as mitigating evidence and that it could give mitigating effect to that evidence in imposing sentence.” 15
We are not writing on a clean slate on this issue. This Court approved identical jury instructions on this point in Miller16 and Emery v. Johnson.17 In Miller, we concluded that the defendant failed to show that the same instructions given by the trial court in this case violated Penry I.We rejected the argument that the jury was prevented from considering the mitigating evidence.18
Miller’s jury, unlike Penry’s, -was instructed that it should consider mitigating evidence when deliberating on the special issues.... [It] was instructed that if it determined when giving effect to the mitigating evidence, if any, that a life sentence rather than a death sentence was an appropriate response to Miller’s personal culpability, a negative finding should be given to the special issue under consideration.19
In the alternative, Penry argues that the jury charge was a “nullification instruction” and was therefore unconstitutional insofar as it instructed jurors to violate their oaths by rendering an untruthful answer to one of the special issues if they wished to give effect to the mitigating evidence presented in this case. We disagree. The jury was not told to disregard the law; rather, it was instructed on how to obey the law, as explained by the Supreme Court in Penry I.
IV
Next, Penry argues that the admission of certain psychiatric testimony and evidence offered by the state at trial violated his Fifth and Sixth Amendment rights.
A.
Penry’s Fifth Amendment challenge involves three categories of psychiatric testimony and evidence presented by the state: 1. the testimony of Dr. Fason admitted during the guilVinnocence phase of trial; 2. the testimony of Dr. Quijano admitted during the punishment phase of trial; and 3. the report of Dr. Peebles describing a court-ordered examination of Penry, which was admitted at the punishment phase of trial.
1.
Penry’s primary challenge is to the testimony of Dr. Fason. Penry contends that Fason’s testimony was based on his court-ordered competency examination of Penry, and that the state’s use of the testimony to argue future dangerousness during the punishment phase violated Pen-ry’s rights under Estelle v. Smith.20 More particularly, Penry argues that his Fifth Amendment privilege against compelled self-incrimination was violated because he *510was not advised before Dr. Fason’s examination of his right to remain silent and that his statements could be used against him at the sentencing proceeding.
On direct appeal, the Texas Court of Criminal Appeals found that Dr. Fason’s testimony fell within the Buchanan v. Kentucky21 exception to Estelle. Under Buchanan, if a defendant presents psychiatric evidence, then the prosecution may present rebuttal psychiatric evidence without violating the Fifth Amendment.
Penry contends that, as applied to this case, proper rebuttal evidence under Buchanan is limited to evidence tending to prove that Penry is not mentally retarded and that the state’s evidence went beyond that scope. After a careful review of the record, we find that Fason’s testimony did fall within the Buchanan exception.
At the guilt/innoeence phase of trial, Penry offered various psychological records, including reports of his performance on a number of psychological and IQ tests. The records also included observations of his emotional status and social behavior. As demonstrated by the closing argument of Penry’s attorney, one reason these records were introduced was to lay a predicate for an argument that Penry’s confessions were not truly voluntary because Penry is mentally retarded and, thus, submissive to authority figures. The evidence was also offered to support Penry’s argument that his mental retardation made him less likely to act with the intent required for capital murder.
Dr. Fason’s testimony was introduced to rebut these arguments. Fason testified that Penry had an antisocial personality disorder. He explained how that condition could affect Penry’s IQ scores, and that it was possible that Penry was not mentally retarded. Also, he testified that someone with an antisocial personality disorder would usually not be easily led by others and would likely disrespect and rebel against authority. Fason did not discuss any statements made by Penry during Fa-son’s examination, except whether Penry was able to identify his attorney at the interview. We disagree with Penry’s characterization of Fason’s testimony as a “sham rebuttal” by the state in order to introduce to the jury the idea that Penry was a “psychopath.” Penry’s defense centered around his diminished capacity — his alleged mental retardation at the time of the offense — and the idea that his mental status rendered his confessions involuntary. Therefore, we conclude that the Court of Criminal Appeals’s determination that Fason’s testimony was proper rebuttal under Buchanan is neither contrary to nor an unreasonable application of clearly established federal law.22
2.
In addition to his challenge to Dr. Fa-son’s guilt phase testimony, Penry also challenges the court’s admission, at the punishment phase, of the testimony of Dr. Quijano and the report of Dr. Peebles as violating Estelle.
At the punishment phase, Penry called various relatives and neighbors who testified that they believed Penry was mentally retarded and abused as a child. He also called Dr. Randall Price, who had reviewed certain portions of Penry’s medical records and administered various psychological tests to Penry. Dr. Price concluded that Penry had a brain impairment and was mentally retarded, and that the mental retardation could have influenced his involvement in criminal activity. Although he admitted that Penry had an antisocial history, he stated that Penry “looks more *511like people with brain damage ... than those with antisocial personality.”
In rebuttal, the state called Doctors Qui-jano and Samenow and introduced into evidence a number of Penry’s mental health records. Dr. Quijano conducted a court-ordered competency examination of Penry. He testified that Penry had an antisocial personality disorder which made him more likely to be violent in the future. However, he testified that he based his opinion only on Penry’s medical records including evaluations by others, and not on his own examination of Penry. Thus, the Texas Court of Criminal Appeals found no Fifth Amendment violation. This finding was not contrary to, nor an unreasonable application of, clearly established federal law.23
The report of Dr. Peebles was admitted into evidence during the punishment phase, and was based on Dr. Pee-bles’s 1977 examination of Penry prior to his trial on an unrelated rape charge. The report determined that Penry would be dangerous in the future if released. At the time of Dr. Peebles’s examination, Penry was not yet in custody on the instant capital charge and, thus, could not have been warned about the potential use of his statements at the punishment phase of the capital trial. The Texas Court of Criminal Appeals found no Fifth Amendment violation because Penry’s attorney had requested the examination; thus, Dr. Peebles was acting as an agent of the defense, not of the state in conducting his examination.24 We cannot say that the court’s conclusion was unreasonable or contrary to Supreme Court precedent.25
B.
Penry also argues that his Sixth Amendment right to effective assistance of counsel was violated by the use of testimony on future dangerousness from Doctors Quijano and Fason because Penry and his counsel were told that their examinations of him were solely for the purpose of determining competency. Under Powell v. Texas, “once a capital defendant is formally charged, the Sixth Amendment right to counsel precludes such an examination without first notifying counsel that ‘the psychiatric examination [will] encompass the issue of their client’s future dangerousness.’ ”26 The Texas Court of Criminal *512Appeals concluded that Penry’s attorney was “on notice that if he intended to put on a ‘mental status’ defense, he would have to anticipate the use of psychological evidence by the prosecution in rebuttal.”27 At a pretrial hearing, the trial court expressly warned Penry’s counsel that the testimony of Doctors Fason and Quijano might be admissible at trial if the defense put on psychiatric evidence.28 At trial, Penry argued that he was mentally retarded; thus, his confessions were involuntary. He also argued that mental retardation could have been a contributing cause of Penry’s violent criminal acts and that his mental retardation mitigated against the imposition of the death penalty. The state was entitled to rebut this evidence by offering psychiatric evidence that some condition other than mental retardation was a more sound explanation for Penry’s conduct. Thus, the Court of Criminal Appeals’s findings are not contrary to, nor an unreasonable application of, clearly established federal law.
V
Penry next contends that his execution would violate the Eighth Amendment, based on his alleged mental retardation and severe child abuse. First, Penry makes a general argument that execution of the mentally retarded is a per se violation of the Eighth Amendment. We agree with the district court that this claim is procedurally barred because Penry did not make the argument in state court. However, even if this claim was not procedurally barred, it has been rejected by the Supreme Court.29
Penry also argues that the death penalty would be cruel and unusual as applied to him personally, because of his mental retardation and severe childhood abuse. This argument also fails. On Pen-ry’s direct appeal, the Texas Court of Criminal Appeals (citing Penry I) concluded that constitutional requirements were met because the jury was able to consider and give effect to Penry’s mitigating evidence before determining that the death sentence was appropriate.30 In Pen-ry’s second trial, he presented extensive mitigating evidence and the jury was instructed to consider that evidence and told how to give it effect. More significantly, although Penry was the individual before the Supreme Court in Penry I, the Court did not suggest that his execution would be unconstitutional based on his mental retardation or childhood abuse. The Texas Court of Criminal Appeals’s conclusion that Penry’s execution would not violate the Eighth Amendment was neither contrary to nor an unreasonable application of clearly established Supreme Court precedent.
VI
Penry makes several other arguments in support of his motion. He contends that: 1. the trial court violated his rights under Simmons v. South Carolina31 by excluding his signed statement waiving any right to parole, while allowing the state to argue future dangerousness; 2. his confessions were taken involuntarily in violation of the Fifth Amendment; and 3. the jury instructions at his competency trial were unconstitutionally vague because they did not define the terns “reasonable,” “rational,” and “understanding.” We find all of these arguments to be unpersuasive, essentially for the reasons given by the district court in its thorough opinion of March 29, 1999.
VII.
For the reasons stated above, we deny Penry’s motion for a certificate of appeala-*513bility. We also vacate the stay of execution previously entered by this court.
. Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989) (“Penry I").
. Penry I, 492 U.S. at 320, 109 S.Ct. at 2947.
. Penry v. State, 903 S.W.2d 715 (Tex.Crim.App.1995).
. 28 U.S.C. § 2253(c)(2); Slack v. McDaniel, — U.S. —, 120 S.Ct. 1595, 1603, 146 L.Ed.2d 542 (2000); United States v. Kimler, 150 F.3d 429, 431 (5th Cir.1998).
. Miller v. Johnson, 200 F.3d 274, 280 (5th Cir.2000) (quoting Barefoot v. Estelle, 463 U.S. 880, 893 n. 4, 103 S.Ct. 3383, 3394 n. 4, 77 L.Ed.2d 1090 (1983)); Hicks v. Johnson, 186 F.3d 634, 636 (5th Cir.1999), cert. denied — U.S. —, 120 S.Ct. 976, 145 L.Ed.2d 844 (2000); see also Slack, 120 S.Ct. at 1603-04 (quoting Barefoot v. Estelle, 463 U.S. 880, 893 and n. 4, 103 S.Ct. 3383, 77 L.Ed.2d 1090).
. Lamb v. Johnson, 179 F.3d 352, 356 (5th Cir.1999), cert. denied — U.S. —, 120 S.Ct. 522, 145 L.Ed.2d 401 (1999).
. Id.-
. See Miller, 200 F.3d at 280-81.
. Williams v. Taylor, — U.S. —, 120 S.Ct. 1495, 146 L.Ed. 2d 389 (2000)
. Id.
. Id.
. 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989).
. The three questions were: 1. Was the conduct of the defendant that caused the death of the deceased committed deliberately and with the reasonable expectation that the death of the deceased or another would result? 2. Is there a probability that the defendant would commit criminal acts of violence that would constitute a continuing threat to society? 3. Was the conduct of the defendant in killing the deceased unreasonable in response to the provocation, if any, by the deceased? Since Penry, the statute has been revised to add a fourth question concerning mitigation.
. Penry v. State, 903 S.W.2d 715, 765 (Tex.Crim.App.1995).
. Penry I, 492 U.S. at 320, 109 S.Ct. at 2947.
. 200 F.3d 274.
. 139 F.3d 191 (5th Cir.1997), cert. denied 525 U.S. 969, 119 S.Ct. 418, 142 L.Ed.2d 339 (1998).
. 200 F.3d at 290.
. Miller, 200 F.3d at 290.
. 451 U.S. 454, 101 S.Ct. 1866, 68 L.Ed.2d 359 (1981). Estelle held that the defendant’s Fifth Amendment right against compelled self-incrimination was violated because he was not told that any statements made during his competency exam could be used against him at the punishment phase on the issue of future dangerousness.
. 483 U.S. 402, 107 S.Ct. 2906, 97 L.Ed.2d 336 (1987).
. See Vardas v. Estelle, 715 F.2d 206, 209-10 (5th Cir.1983) (finding no violation of defendant’s Fifth Amendment privilege because state psychiatrists’ testimony was proper as rebuttal to defendant’s insanity defense; psychiatrists testified that defendant was not insane, but instead was a sociopath.).
. See Williams v. Lynaugh, 809 F.2d 1063, 1068 (5th Cir.1987) (finding no factual basis for Fifth Amendment violation where state psychologist’s testimony on future dangerousness was not based on his interview with the defendant.) See also Hughes v. Johnson, 191 F.3d 607, 616-17 (5th Cir.1999) (finding reasonable a state court's conclusion that psychiatrist’s testimony did not violate Estelle, despite his having conducted a prior improper interview, because it did not influence his testimony; also rejecting idea that “taint” of prior improper interview created absolute bar to any expression of opinion by that psychiatrist); cf. Flores v. Johnson, 210 F.3d 456, 462-70 (5th Cir.2000) (Emilio M. Garza, J., specially concurring) (following but questioning Supreme Court authority allowing psychiatric testimony on future dangerousness deduced without examining the defendant).
. Penry, 903 S.W.2d. at 759-60; see Nelson v. State, 848 S.W.2d 126, 135 (Tex.Crim.App.1992); Estelle, 451 U.S. at 467-68, 101 S.Ct. at 1875-76 (noting that the defendant there did not initiate the examination and was not faced with a person acting solely in his interest).
. See Buchanan v. Kentucky, 483 U.S. 402, 422-23, 107 S.Ct. 2906, 2917-18, 97 L.Ed.2d 336 (1987) (finding that “if a defendant requests [the psychiatric] evaluation or presents psychiatric evidence ... the prosecution may rebut this presentation with evidence from the reports of the examination that the defendant requested. The defendant would have no Fifth Amendment privilege against the introduction of this psychiatric testimony by the prosecution.”). (Emphasis added); see also Schneider v. Lynaugh, 835 F.2d 570, 577 (5th Cir.1988) (finding that, under Buchanan, the fact that defendant requested the competency examination militated against the defendant’s assertion of the Fifth Amendment privilege, particularly when defendant had also introduced psychological evidence.).
. 492 U.S. 680, 681, 109 S.Ct. 3146, 3148, 106 L.Ed.2d 551 (1989) (quoting Estelle, 451 U.S. at 471, 101 S.Ct. at 1877).
. Penry, 903 S.W.2d at 758.
. Id. at 759, n. 46.
. See Andrews v. Collins, 21 F.3d 612, 632 (5th Cir.1994), cert. denied 513 U.S. 1114, 115 S.Ct. 908, 130 L.Ed.2d 790 (1995) (citing Penry I).
. Penry, 903 S.W.2d at 766-67.
. 512 U.S. 154, 114 S.Ct. 2187, 129 L.Ed.2d 133 (1994).