Petitioner who was sentenced to death in a state capital murder trial appeals denial of federal habeas relief. The district court dismissed with prejudice the petitioner’s application for writ of habeas corpus leaving its previously granted stay of execution in effect pending appeal. It granted a certificate of probable cause and petitioner timely appealed. Petitioner urges error under Penry v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989). Concluding that the disposition of this matter is directed by our recent en banc decision in Graham v. Collins, 950 F.2d 1009 (5th Cir.) (en banc), cert. granted, — U.S. -, 112 S.Ct. 2937, 119 L.Ed.2d 563 (1992), we affirm the district court.

Background

Stewart and an accomplice, Kelvin Kelley, decided to rob Donna Kate Thomas in her apartment after they noticed her apartment door ajar. During the course of the burglary the men attempted a sexual offense and ultimately murdered the victim. Each man confessed to a version of the offense in which the other was implicated as the principal actor. Stewart’s prosecution was based on Kelley’s testimony which was corroborated by the testimony of the victim’s young daughter and other state witnesses.

Stewart was convicted by a jury for capital- murder committed during the burglary of a habitation. During the sentencing phase of the trial, the jury responded affirmatively .to the two special issues submitted in accordance with Tex. Code Crim.Proc. Ann. Art. 37.071, and punishment was assessed at death. His conviction was affirmed, 686 S.W.2d 118, and he applied to the district court for the Great Writ and a stay. A stay was granted but the writ was subsequently denied.

Stewart argues on appeal, that in responding to the statutory punishment phase issues, the jury was unable to consider and give mitigating effect to his self-described, non-triggerman role in the commission of the offense. Stewart characterized himself as a lookout man who did not intend to kill the victim and did not assume an active role in the murder. The district court correctly concluded that, if the jury believed that Stewart was not the trigger-man, the jury could give effect to that understanding of the evidence in answering the punishment phase issues.

Analysis

Penry v. Lynaugh held that where mitigating evidence has relevance to moral culpability beyond the scope of the Texas death penalty statute’s special issues, unless special instructions are given, the jury is unable to express its reasoned moral response in determining whether death is an appropriate punishment. Penry, 492 U.S. at 318-19, 109 S.Ct. at 2946-47. In Graham v. Collins, however, this Court held that Penry “does not invalidate the Texas statutory scheme, and that Jurek ^[1] continues to apply, in instances where[*201] no major mitigating thrust of the evidence is substantially beyond the scope of all the special issues.” 950 F.2d at 1027. In Stewart’s case, the first special issue ^[2] clearly encompasses any evidence that he was merely an accomplice in the killing and lacked the intent to kill. The first special issue inquires solely into Stewart’s conduct. The law of parties ^[3] is not even applied to the punishment deliberations. ^[4] In fact, the record shows that during the punishment phase, counsel for Stewart argued to the jury that it should consider, when responding to the special issues, whether Stewart was in fact the triggerman or merely an accomplice. “Although a reasonable juror might have found that this evidence had independent mitigating value in reducing moral culpability, we cannot say with assurance that a major mitigating thrust of the evidence was substantially beyond the reach of the deliberateness issue.” See Demouchette v. Collins, 972 F.2d 651 (5th Cir.1992). Thus, the jury required no separate instruction.

Stewart’s argument that the jury was precluded from considering this evidence as a mitigating factor under the future dangerousness issue in the second special issue is equally unavailing. Given counsel’s arguments to the jury during the punishment phase, the petitioner has not shown that the jury was precluded from considering his status as non-triggerman. Id.

Stewart does not satisfy his burden of demonstrating a “reasonable likelihood that the jury ... applied] the challenged instructions in a way that prevented] the consideration of constitutionally relevant evidence.” Boyde v. California, 494 U.S. 370, 371, 110 S.Ct. 1190, 1191, 108 L.Ed.2d 316 (1990). The punishment phase issues allowed the jury to give mitigating effect to Stewart’s alleged non-triggerman status if they chose to credit his version of the offense.

Finally, although not clear from the petitioner’s brief, to the extent that he challenges the district court’s ruling regarding whether or not Stewart had the requisite mental state for culpability established in Enmund v. Florida, 458 U.S. 782, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982), we affirm the holding of the district court finding that the jury verdict and its answers to the special issues together with the Court of Criminal Appeals’ holding satisfy Enmund and Cabana v. Bullock, 474 U.S. 376, 106 S.Ct. 689, 88 L.Ed.2d 704 (1986).

Accordingly, the judgment of the district court denying habeás relief is affirmed and the stay of execution issued by the district court is lifted. . .