Lawyers for Artez Hammonds want a new trial. They say he was poorly represented the first time.
Hammonds was convicted of raping and killing Marilyn Mitchell. The case went unsolved for years.
Hammonds was already in prison for trying to kill another woman when DNA evidence linked him to the 1990 Mitchell murder.
Early last year, defense attorneys tried to have the death penalty case reversed on appeal by claiming the state illegally took Hammonds blood for DNA tests.
But the U.S. Supreme Court and the State Court of Criminal Appeals refused to overturn the trial court ruling.
Hammonds is being held on death row in Holman Prison in Atmore, Alabama.
His hearing is scheduled for Friday at 1 p.m.
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