Billy Ray Nelson was convicted of capital murder and sentenced to death in December 1991 for murdering Charla Wheat. Nelson filed a petition for a writ of habeas corpus in federal district court pursuant to 28 U.S.C. § 2254 (2000). Nelson’s petition raised eleven issues which he contended provided a basis for a writ of habeas corpus to issue. Appellee moved for summary judgment on all eleven issues. The district court granted summary judgment and denied Nelson’s petition. The district court also refused to grant a certificate of appealability (“COA”) on any of the issues raised by Nelson.
Nelson now seeks a COA from this court on three issues: (1) whether the special issue instructions used at trial provided the jury with an adequate vehicle to give mitigating effect to evidence in violation of the Eighth and Fourteenth Amendments as construed in Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989); (2) whether Nelson’s counsel provided ineffective assistance by failing to request an instruction on the definition of reasonable doubt or by failing to raise this issue on direct appeal; and (3) whether the introduction of testimony by a state psychiatrist regarding future dangerousness violated the Fifth Amendment as construed in Estelle v. Smith, 451 U.S. 454, 101 S.Ct. 1866, 68 L.Ed.2d 359 (1981). We grant a COA on the first two issues but deny the application for COA on the other issue. With respect to the merits issues, we affirm the district court’s denial of habeas relief.
BACKGROUND
Nelson was indicted for the capital murder of Charla M. Wheat and the attempted capital murder of Wheat’s roommate Carol Maynard that occurred on or about February 23, 1991. In December 1991, Nelson was tried for the capital murder of Wheat. During the guilt/innocence phase of trial Maynard testified as to the events of February 23. Specifically, Maynard testified that she and Wheat were forced, at knife-point, by Nelson to perform sexual acts on each other and on Nelson. Maynard further testified that Nelson stabbed Wheat. Other testimony established that the stab wounds were the cause of Wheat’s death. Also, at trial, two voluntary statements made by Nelson were admitted into evidence. In these statements Nelson confessed to stabbing Wheat. He stated that he committed the crime because he “was drunk and wanted a piece of butt.”
On December 11, 1991, the jury found Nelson guilty of capital murder. On December 13, following the punishment phase of trial, the jury answered affirmatively the two special issues submitted pursuant to Texas Code of Criminal Procedure article 37.071(b). Nelson was sentenced to death. Nelson’s sentence and conviction were affirmed on direct appeal by the Texas Court of Criminal Appeals on May 26, 1993. The United States Supreme Court denied Nelson’s petition for writ of certiorari on March 21,1994.
On April 17, 1997, Nelson commenced a series of state applications for writ of habeas corpus. The state district court issued findings of fact and conclusions of law *212recommending denial of relief on all of Nelson’s claims on July 10, 2001. The Court of Criminal Appeals denied Nelson’s application on the findings and recommendations of the trial court. Additionally, it dismissed Nelson’s subsequent application as an abuse of the writ under Texas Code of Criminal Procedure article 11.071, § 5(a).
DISCUSSION
Nelson’s § 2254 habeas petition, filed on December 7, 2001, is subject to the Anti-terrorism and Effective Death Penalty Act of 1996 (AEDPA). See Penry v. Johnson, 532 U.S. 782, 792, 121 S.Ct. 1910, 150 L.Ed.2d 9 (2001). Under AEDPA, Nelson must obtain a COA before he can appeal the district court’s denial of habeas relief. 28 U.S.C. § 2253(c)(1) (2000); Slack v. McDaniel, 529 U.S. 473, 478, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). “[U]ntil a COA has been issued federal courts of appeals lack jurisdiction to rule on the merits of appeals from habeas petitioners.” Miller-El v. Cockrell, 537 U.S. 322, 123 S.Ct. 1029, 1039, 154 L.Ed.2d 931 (2003).
To obtain a COA, Nelson must make “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2) (2000); Miller-El, 123 S.Ct. at 1039; Slack, 529 U.S. at 483, 120 S.Ct. 1595. To make such a showing, he must demonstrate that “reasonable jurists could debate whether (or, for that matter, agree that) the petition should have been resolved in a different manner or that the issues presented were adequate to deserve encouragement to proceed further.” Miller-El, 123 S.Ct. at 1039 (quoting Slack, 529 U.S. at 484, 120 S.Ct. 1595).
In Miller-El, the Supreme Court instructed, as it had previously held in Slack, that federal courts should “limit [their] examination to a threshold inquiry into the underlying merit of [the petitioner’s] claims.” Miller-El, 123 S.Ct. at 1034. The Court observed that “a COA ruling is not the occasion for a ruling on the merit of petitioner’s claim ...” Id. at 1036. Instead, our determination must be based on “an overview of the claims in the habeas petition and a general assessment of their merits.” Id. at 1039. “This threshold inquiry does not require full consideration of the factual or legal bases adduced in support of the claims.” Id. We do not have jurisdiction to justify the denial of a COA based on an adjudication of the actual merits of the claims. Id. Accordingly, we cannot deny an “application for a COA merely because [we believe] the applicant will not demonstrate an entitlement to relief.” Id. “[A] claim can be debatable even though every jurist of reason might agree, after the COA has been granted and the case has received full consideration, that petitioner will not prevail.” Id.
Because the district court denied relief on the merits of the claims for which Nelson seeks a COA, he “must demonstrate that reasonable jurists would find the district court’s assessment of the constitutional claims debatable or wrong.” Barraza v. Cockrell, 330 F.3d 349, 351 (5th Cir.2003) (quoting Miller-El, 123 S.Ct. at 1040). Nelson first seeks a COA on the ground that the special issue instructions given to the jury at sentencing failed to provide an adequate vehicle to give effect to his mitigating evidence in violation of Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989). The instructions given by the trial court were identical to those given in Penry. To grant relief on Nelson’s Penry claim, we must determine that “(1) that the proffered evidence was constitutionally relevant mitigating evidence, and, if so, (2) that the proffered evidence was beyond the ‘effective reach’ of the jurors.” Madden v. Collins, 18 F.3d 304, 308 (5th Cir.1994).
*213In this case, Nelson argued that the following evidence is mitigating: (1) Nelson’s rejection by his mother, (2) Nelson’s abuse of and addiction to drugs and alcohol, (8) Nelson’s troubled relationships with his brother and women, and (4) that he suffered from a treatable borderline personality disorder. We conclude that reasonable jurists could debate the district court’s conclusion to deny relief on the Penry claim and accordingly grant Nelson a COA on this claim.
Although we grant a COA, we conclude that the district court properly denied relief on Nelson’s Penry claim. None of Nelson’s evidence is incapable of being assessed and assigned full mitigating weight under the charge presented to his jury. Thus, the unusual problem presented in Penry, whereby evidence of extreme childhood abuse and mental retardation were held to be potentially mitigating but beyond the scope of the statutory death penalty issues, does not exist here. This court has repeatedly held that substance addiction is not Penry-type evidence. Robertson v. Cockrell, 825 F.3d 243, 253-54 (5th Cir.2003) (en banc). Furthermore, we have held that evidence of mental disease that, like Nelson’s borderline personality disorder, can be controlled with medication and treatment, can be given full mitigating effect via the special issues. Id. at 252 (discussing Hernandez v. Johnson, 248 F.3d 344 (5th Cir.2001)); see also Robison v. Johnson, 151 F.3d 256, 266-67 (5th Cir.1998); Lucas v. Johnson, 132 F.3d 1069, 1082-83 (5th Cir.1998). In addition, this court has repeatedly found evidence of childhood abuse and neglect far more severe than that suffered by Nelson because of his mother’s rejecting him not to be constitutionally relevant. See Robertson, 325 F.3d at 253; Davis v. Scott, 51 F.3d 457, 462 (5th Cir.1995); Madden, 18 F.3d at 308; Barnard v. Collins, 958 F.2d 634, 639 (5th Cir.1992).
Nelson, in passing, also points to evidence of organic brain damage which, he urges, the special issues did not provide a vehicle to consider. We disagree. The only record evidence of organic brain damage is a single sentence of testimony from an expert witness for the defense, stating “there is minimal room to consider that there may be minimal brain damage.” The expert, however, explicitly said that he could not make a formal diagnosis that Nelson in fact had brain damage. He only suggested that if further medical examinations were performed, the existence of brain damage should not be ruled out prior to the exam. Additionally, no evidence suggested that even if there was brain damage, Nelson’s acts were caused by it. Thus, this evidence is not constitutionally relevant. See Robertson, 325 F.3d at 253 (stating that for evidence to fall within the scope of Penry, there must be a causal nexus between the mitigating evidence and the commission of the crime); Graham v. Collins, 950 F.2d 1009, 1029 (5th Cir.1992) (en banc) (holding that the relevant inquiry is whether the criminal act was “due to the uniquely severe permanent handicaps with which the defendant was burdened through no fault of his own”).
“Under AEDPA, a federal court may grant a prisoner’s petition only where the state court’s ‘decision’ was ‘contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States’ or was ‘based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.’ ” Santellan v. Cockrell, 271 F.3d 190, 192 (5th Cir.2001) (quoting 28 U.S.C. § 2254(d) (2000)), cert. denied, 535 U.S. 982, 122 S.Ct. 1463, 152 L.Ed.2d 461 (2002). Based on this standard and the *214nature of Nelson’s proffered evidence, we cannot say that the Court of Criminal Appeals unreasonably applied clearly established federal law in rejecting Nelson’s Penny claim. Therefore, we affirm the district court’s denial of relief on this claim.
Nelson next seeks a COA on his claim that his trial counsel was ineffective for failing to object to the jury charge used during the sentencing phase of Nelson’s trial because the court failed to include a definition for the phrase “reasonable doubt.” At the time of his trial in December 1991, Texas courts were required to include a definition of “reasonable doubt” in the jury charge. Geesa v. State, 820 S.W.2d 154 (Tex.Crim.App.1991), overruled by Paulson v. State, 28 S.W.3d 570 (Tex.Crim.App.2000). The definition requirement was not statutory; it was mandated by the Texas Court of Criminal Appeals as an interpretation of the United States Constitution. Id. at 161-62. The definition was required even in the absence of a request by either party. Id. at 162. The failure to include the definition constituted reversible error even without a contemporaneous objection. Reyes v. State, 938 S.W.2d 718, 721 (Tex.Crim.App. 1996), overruled by Paulson, 28 S.W.3d 570. Because reasonable jurists could debate the district court’s reasoning denying relief on this claim, we grant Nelson a COA
To establish an ineffective assistance of counsel claim, Nelson must show that his counsel’s performance was deficient and that he was actually prejudiced by the deficient performance. Strickland, 466 U.S. at 687, 104 S.Ct. 2052. Whether counsel’s performance was deficient is determined by examining whether the challenged representation fell below an objective standard of reasonableness. Kitchens v. Johnson, 190 F.3d 698, 701 (5th Cir. 1999). Nelson must also establish that the “prejudice caused by the deficiency is such that there is a reasonable probability that the result of the proceedings would have been different.” Ransom v. Johnson, 126 F.3d 716, 721 (5th Cir.1997). Nelson must show that the prejudice rendered the sentencing “fundamentally unfair or unreliable.” Id. (quoting Lockhart v. Fretwell, 506 U.S. 364, 369, 113 S.Ct. 838, 122 L.Ed.2d 180 (1993)).
Assuming arguendo that Nelson’s trial counsel was deficient in failing to object to the exclusion of the “reasonable doubt” definition in the sentencing phase jury charge, nevertheless, Nelson was not prejudiced by the absence of the definition in the jury charge used at the sentencing phase. Nelson argues that his trial counsel’s failure to request the definition was prejudicial because he lost the protection of a definition on reasonable doubt. We disagree. The jury was given the Geesa definition during the guilt/innocence phase of trial just a couple of days before the jury began its deliberations regarding punishment. Furthermore, Nelson’s counsel discussed the definition of reasonable doubt from the guilVinnocence phase of trial during closing arguments in the punishment phase. Given that the jury had the benefit of a definition of reasonable doubt, Nelson was not prejudiced by the failure to have the definition repeated in the punishment phase jury charge.1 Thus, the state court did not unreasonably apply *215clearly established federal law in rejecting Nelson’s ineffective assistance of trial counsel claim.
Nelson goes on to argue that his appellate counsel was ineffective for failing to raise the omission of the Geesa definition on direct appeal. Nelson argues, citing Geesa and Reyes, that had his counsel raised the issue, he would have been automatically entitled to a reversal of his conviction and a new trial.
Even if Nelson’s position is correct as a matter of Texas law at one time, his counsel’s appellate error still cannot be prejudicial for Strickland purposes. This is because the prejudice prong is determined by current law and not the law that existed at the time of trial. Westley v. Johnson, 83 F.3d 714, 723 (5th Cir.1996) (citing Lockhart, 506 U.S. at 372-73, 113 S.Ct. 838). Strickland prejudice “focuses on the question whether counsel’s deficient performance renders the result of the trial unreliable or the proceeding fundamentally unfair. Unreliability or unfairness does not result if the ineffectiveness of counsel does not deprive the defendant of any substantive or procedural right to which the law entitles him.” Lockhart, 506 U.S. at 372, 113 S.Ct. 838. As noted previously, the Texas Court of Criminal Appeals overruled Geesa in 2000. Paulson, 28 S.W.3d at 573. Therefore, the omission of the Geesa definition cannot be prejudicial for purposes of Strickland. We affirm the district court’s denial of relief on Nelson’s Geesa-based ineffectiveness claims.
Nelson also seeks a COA with respect to his claim that a psychiatric examination performed by Dr. James Grigson on behalf of the State of Texas violated the Fifth Amendment because Nelson was not advised that he had the right to remain silent and that any statements he made could be used against him during the sentencing phase of his trial. See Estelle, 451 U.S. at 467-68, 101 S.Ct. 1866 (holding that testimony by a psychiatrist on behalf of the state is inadmissible when the defendant is not advised of his right to remain silent during a pretrial examination by the state’s psychiatrist). Thus, Nelson argues that the trial court should have excluded Dr. Grigson’s trial testimony about Nelson’s future dangerousness.
Nelson concedes that as his trial counsel failed to object to Grigson’s testimony, this claim is procedurally defaulted unless he can demonstrate cause for the default and actual prejudice as a result of the alleged violation of federal law. See Ogan v. Cockrell, 297 F.3d 349, 356 (5th Cir.), cert. denied, 537 U.S. 1040, 123 S.Ct. 582, 154 L.Ed.2d 464 (2002). In his application for COA, Nelson argues that he can establish cause based on his claim that his trial counsel was constitutionally ineffective for failing to object to Grigson’s testimony on Fifth Amendment grounds. See Murray v. Carrier, 477 U.S. at 488-89, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986); Dowthitt v. Johnson, 230 F.3d 733, 752 (5th Cir.2000). We disagree.
Although Nelson did raise in the state habeas proceeding an ineffective assistance claim based on his counsel’s failure to make an Estelle objection at trial, he did not raise this claim before the federal district court. ‘We have repeatedly held that a contention not raised by a habeas petitioner in the district court cannot be considered for the first time on appeal from that court’s denial of habeas relief.” Johnson v. Puckett, 176 F.3d 809, 814 (5th Cir.1999) (quoting Johnson v. Puckett, 930 F.2d 445, 448 (5th Cir.1991)). Having failed to raise his ineffective assistance claim before the district court, Nelson cannot now rely upon this claim to establish cause for the default. See Edwards v. Carpenter, 529 U.S. 446, 452-53, 120 S.Ct. 1587, 146 L.Ed.2d 518 (2000) *216(holding that an ineffective assistance claim asserted as cause for the procedural default of another claim can itself be procedurally defaulted and thus cannot serve as cause to excuse the default of the other claim); Stewart v. Lagrand, 526 U.S. 115, 120, 119 S.Ct. 1018, 143 L.Ed.2d 196 (1999) (per curiam) (holding that ineffective assistance claim cannot serve as cause when petitioner waived ineffective assistance claim before federal district court). Since reasonable jurists would not debate or find wrong that Nelson has procedurally defaulted his Estelle claim, we deny his application for COA on this issue.
CONCLUSION
With respect to Nelson’s Penry claim and ineffective assistance claims relating to the Geesa definition, we grant his application for COA. We conclude, however, that the district court did not err in denying habeas relief on these claims because the state courts’ application of clearly established federal law was not objectively unreasonable. We deny Nelson’s application for COA on his claim related to Dr. Grigson’s testimony and as such lack jurisdiction to review the district court’s denial of habeas relief on this claim.
AFFIRMED; COA DENIED.
Pursuant to 5th Cir. R. 47.5, the Court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.
. Contrary to Nelson’s additional argument, the failure to object did not preclude Nelson’s counsel from raising the omission of the definition from the charge on appeal because under Texas law, a trial court’s omission of the definition was non-waivable and could be raised on appeal even in the absence of an objection at trial. Reyes, 938 S.W.2d at 721. Failure to object did not prejudice Nelson on appeal.