PER CURIAM:

This is an application for certificate of appealability from a judgment of a federal district court refusing to set aside a state conviction of capital murder.

I

Eugene Alvin Broxton in April 1992 was convicted by a Texas jury in Harris County, Texas, of capital murder and shortly thereafter sentenced to death. The Texas Court of Criminal Appeals confirmed the conviction and sentence. Broxton v. State, 909 S.W.2d 912 (Tex.Crim.App. 1995). Broxton did not file a petition for writ of certiorari in the United States Supreme Court.

In 1997, Broxton filed an application for state writ of habeas corpus, and, after an evidentiary hearing, the state habeas trial court filed findings of fact and conclusions of law together with a recommendation that relief be denied. In October, 1999, the Texas Court of Criminal Appeals adopted those findings and conclusions and denied relief. Ex Parte Broxton, Application No. 42,781-01 (Texas Crim.App. October 27, 1999).

In November 1999, the United States District Court for the Southern District of Texas, granted Broxton's request for appointment of counsel pursuant to 21 U.S.C. § 848(q), and in March of 2000 Broxton filed his petition for writ of habeas corpus in that court, supplementing that petition in June. Broxton raised four claims in his petition before the federal trial court: (1) trial counsel rendered ineffective assistance by failing to preserve error when the trial court limited the cross-examination of witness Waylon Dockens; (2) appellate counsel rendered ineffective assistance by (a) failing to raise on appeal alleged trial court error in refusing to allow a lesser-included offense instruction and (b) failing to raise the allegedly improper denial of a challenge for cause against prospective juror James Smith; (3) his rights were violated when the trial court failed to instruct the jurors on the definition of "life sentence;" and (4) the Texas death penalty scheme is administered in violation of the Eighth Amendment. By his supplement to his petition he asserted that his sentencing proceedings were tainted by the State's expert whose opinion considered race as a relevant circumstance for the jury's sentencing decision.

The federal district court sustained the claim that constitutional error tainted the punishment phase of the trial and vacated the death sentence. At the same time, it rejected all claims aimed at the guilt finding, declining to upset the verdict and judgment finding Broxton guilty of capital murder. The district court ordered the State of Texas to release Broxton from custody unless within 180 days the State either imposed a sentence of life imprisonment or conducted a new sentencing hearing. It further provided that the 180-day time period did not commence until "the conclusion of any appeal in the portion of this order that denies federal habeas relief." Finally, the district court refused to grant Broxton a certificate of appealability.

II

Broxton seeks to appeal the denial of relief from the finding of guilt and petitions this court for a certificate of appealability. The set-aside of the death sentence is not before us. Broxton argues that his trial counsel rendered ineffective assistance by not preserving an asserted error of the trial court in limiting the cross-examination of witness Waylon Dockens and in not raising on appeal the refusal of the state trial judge to instruct on the lesser included offense of felony murder.

We are persuaded that these claims lack sufficient merit to warrant a certificate of appealability, and that application is denied. We do so for essentially the same reasons recited by the United States District Court in its order filed March 28, 2001.

III

As the federal district court described in its order, Waylon and Sheila Dockens were guests at the Magnolia Hotel in 1991. Broxton pushed his way into their hotel room and proceeded to rob them, using a .44 magnum pistol belonging to Waylon. He struck both with the pistol and then shot them. Waylon was shot in the face and Sheila died of a gunshot wound that entered her upper left arm, striking vital organs before exiting her body.

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The first claim, the limitation of the cross-examination of Waylon Dockens, is meritless. The state trial judge allowed defense counsel to elicit from Waylon at trial that he was thinking of filing suit against the hotel, but refused to allow counsel to pursue the matter further, concluding that it was not relevant. The state habeas court and the federal district court found that the ruling was not prejudicial, even if error, because the jury plainly had before it an even larger interest of Waylon Dockens in the outcome of the prosecution — he was beaten and shot by Broxton and his wife was slain by him. Not allowing the defense to further develop facts surrounding a possible lawsuit against the hotel did not constitutionally curtail the cross-examination of the witness.

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The second contention, attacking the effectiveness of his appellate counsel in not raising on appeal the absence of an instruction on a lesser included offense, is equally meritless. Given the circumstances of this crime, the lesser included offense of felony murder was not in the case, as explained by the courts below. It follows that the first prong of Strickland was not met. Strickland v. Washington, 466 U.S. 668, 697, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

IV

The application for certificate of appealability is denied.