Rodney Rachal has been on death row since March 1993 for the robbery and fatal shooting of Charles Washington at a Houston apartment complex in 1990.
Rachal's trial in October 1992 came during a time before guidelines covering punishment phases of capital murder trials were refined by rulings from the U.S. Supreme Court.
The appeals court in 2009 asked his trial court to review the case. The Austin court's decision Wednesday backed the findings of the trial court that the 41-year-old Rachal deserves a new punishment hearing.
There was evidence that Rachel was a troubled and impoverished youth.