The Florida Supreme Court last month ordered the hearing in the
case of 61-year-old Manuel Valle, convicted in the 1978 shooting
death of Coral Gables police officer Louis Pena.
Valle's scheduled execution Tuesday was stayed for a month to allow arguments over Florida's plan to use pentobarbital in place of another drug experiencing a shortage.
Valle's lawyers contend he could feel pain or harm because the drug has never been extensively tested on humans. It has been used in other states but never in Florida. Pentobarbital renders a person unconscious.
The judge's ruling is expected by Friday.