A death row prisoner is appealing against his sentence because he says his lawyer kept dozing off.
Calvin Burdine claims he did not receive a fair trial because of his lawyer's courtroom naps.
At a previous appeal hearing, three judges ruled that the lawyer's naps did not violate Burdine's rights in the 1984 case.
All 14 judges on the New Orleans-based Fifth US Circuit Court of Appeals are to hear arguments by Burdine's new lawyers and the Texas attorney general's office on whether the October ruling should be overturned.
Burdine, 47, has spent 16 years on the Texas death row for fatally stabbing his gay lover with a butcher knife, a crime he says he did not commit.
He came within moments of execution in 1987 before receiving a court-ordered reprieve, and the case has bolstered arguments by death penalty opponents who also claim legal representation for defendants who cannot afford their own lawyers is inadequate.
Burdine was accused of killing 50-year-old WT Wise on April, 18, 1983, while stealing from a trailer they shared near Houston. He denies killing Wise but acknowledges he was at the scene with an accomplice, who served eight years in prison for a lesser murder charge.
At a 1995 hearing, three jurors and a court reporter testified that Burdine's now-deceased lawyer, Joe Cannon, often napped for as long as 10 minutes during his trial.
US District Judge David Hittner in Houston ruled Burdine did not receive a fair trial and ordered the state to retry him or set him free, but the Fifth Circuit ordered the former nurse to remain in prison while it considered the case.
The three-judge panel said in its opinion last October that Burdine's conviction should stand because he was unable to show exactly when Cannon slept during critical parts of the trial. Burdine's lawyers appealed to the full Fifth Circuit.