Donald Verrilli, an attorney for the Kentucky inmates, has said, "It really is not about fine-tuning the system to create an incrementally less amount of pain. This is about avoiding torture."
But in court, the justices seemed skeptical of the argument. Conservative Justice Antonin Scalia said, "Where does this come from that you must find the method of execution that causes the least pain? We have approved electrocution. We have approved death by firing squad. I expect both of those have more possibilities of painful death than the protocol here."
There have been instances across the country of fumbled executions.
In Florida, convicted murderer Angel Diaz was executed in 2006. But a medical examiner's postmortem examination revealed that due to the improper injection of the anesthetic in his case, he had chemical burns on both arms. Experts believe he would have felt extreme pain for 20 to 30 minutes.
In Ohio, Joseph Clark was sentenced to death for killing a gas station attendant. But his 2006 execution was botched. It took him 86 minutes to die while he screamed in pain.
Even his victim's brother, Michael Manning, watched in horror. "He started to shake his head from side to side," said Manning. It took a technician 19 tries to insert the deadly intravenous needle.
Manning said what he saw in that execution chamber should not have happened. "I believe in the death penalty, but I side on the constitutionality side of it. The Eighth Amendment says no cruel and unusual punishment, and that's what I think it was."
In Missouri, the doctor who devised and supervised that state's lethal injection procedure has admitted in court that he is dyslexic, "so it's not unusual for me to make mistakes."
An investigation by the St. Louis Post-Dispatch revealed that the doctor, Alan R. Doerhoff, had been sued for malpractice more than 20 times. The paper also reported that one nurse who worked on Missouri executions is himself a convicted stalker.
But victims' rights advocates, as well as victims' family members, often have little sympathy for the arguments of the death row inmates.
Dennis Briscoe was 14 years old when Baze opened fire with an assault weapon and murdered his father and uncle -- both Kentucky law enforcement officers.
"What they should really consider is the pain my father and uncle went through when that happened," he said. "We should all be so lucky as to just fall asleep when we die."