NEW ORLEANS—Attorneys for a former University of Texas honors student who has been on death row for three decades for killing an Austin police officer again asked an appeals court Tuesday to throw out his sentence.

David Lee Powell, 57, has been sentenced to death three times for the 1978 killing of Ralph Albanedo, who had pulled over Powell’s girlfriend for not having a proper license plate on her car. Powell was a passenger in the car.

Albanedo was shot 10 times by an automatic assault weapon.

Powell has been on death row since October 1978, the month following his conviction. Only five other Texas inmates have spent more time there.

His case has wound through a long path in the courts.

His original conviction was vacated by the U.S. Supreme Court and returned to the Texas Court of Criminal Appeals. After the state court reaffirmed his conviction and death sentence, the Supreme Court tossed the sentence. In 1991, he was convicted again and sentenced to death, but the second sentence was thrown out by the Court of Criminal Appeals because of improper jury instructions.

By then, Texas law required only a retrial of the punishment phase, which resulted in a third death sentence in 1999.

Powell’s attorneys told a three-judge panel of the 5th U.S. Circuit Court of Appeals on Tuesday that prosecutors did not timely deliver documents that showed Powell’s girlfriend, Sheila Meinert, may have tossed a hand grenade and fired during a standoff after Albanedo’s shooting.

During the third trial, defense attorneys were trying to show that Powell did not pose a future danger, one of the conditions jurors must decide before issuing a death sentence.

Attorney Richard Burr said that when prosecutors tried to prove a future danger, they contended Powell threw the grenade. But he said 11 police officers, in a letter to the Texas Board of Pardons and Paroles, opposed Meinert’s later parole on the grounds that she had thrown the explosive. Meinert served four years of a 15-year sentence for being a party to capital murder.

Assistant Texas Attorney General Tina Miranda said most letters opposing parole are signed by people who don’t know many of the facts of a case. She also said the death sentence “hinged on the atrociousness of killing an officer with a fully automatic weapon and then going to another scene and shooting again.”

Another attorney for Powell, Eric Albritton, said a full new trial should be ordered because prosecutors did not submit all the needed elements to the jury for a death sentence to be returned.