A judge in Alabama will decide if a new method of execution using pure nitrogen gas can be used for the first time.
Two other states are considering the method as an alternative to lethal injections, after a spate of botched executions in the US.
But lawyers for Kenneth Eugene Smith, convicted of a 1988 murder, argued the method was unconstitutionally cruel.
They urged the judge to block his 25 January execution using nitrogen hypoxia.
According to Alabama's execution protocol, the nitrogen would be administered for at least 15 minutes or five minutes following a flatline indication on the EKG, whichever is longer.