The court announced it was taking the cases on Monday, and will hear them in the term that begins next October.
The court on a 5 to 4 vote in March issued a last-minute stay to the planned execution of 49-year-old Russell Bucklew, who suffers from a rare disease called cavernous hemangioma. It causes blood-filled tumors to grow in his head, neck and throat, which his lawyers say could rupture during the state's lethal injection process.
Bucklew's attorneys have said Missouri should execute him using nitrogen gas rather than lethal injection, a method that has been floated elsewhere but never used by a state seeking to execute someone.
Earlier this year, Oklahoma said that it would become the first state to use nitrogen gas for all executions going forward, a dramatic response to the inability of states nationwide to obtain the drugs used for lethal injections. Mississippi last year adopted nitrogen gas as a potential method of execution there.
Bucklew is not contesting his conviction for a particularly gruesome crime.
In 1996, Bucklew stalked his former girlfriend to another man's trailer. He shot the man, tried to shoot the woman's fleeing child and then captured the woman. He handcuffed and raped her, then wounded a police officer in a subsequent gunfight.
Bucklew later escaped from jail and attacked the rape victim's mother with a hammer before he was recaptured.
In a brief to the court, Missouri Attorney General Joshua D. Hawley said Bucklew is simply trying to prolong his execution, and has not presented verifiable evidence that another manner of death would prevent suffering.
While Missouri's law authorizes the use of lethal gas, "the state has no protocol in place . . . because that method has not been used since 1965," Hawley wrote. "The state's only gas chamber not only is inoperable; it sits in a museum."
Bucklew's lawyer, Robert N. Hochman, says Bucklew's actions should not justify an indifference from society that he might suffer during execution.
"We refuse to punish with cruelty to protect ourselves against being party to cruelty," they write. "We do so even when the temptation is powerful because the crime we are punishing was itself barbaric and cruel."
In accepting the case, the justices told the state and Bucklew's lawyers that they should address whether Bucklew has met the burden, announced in a previous death penalty case, "to prove what procedures would be used to administer his proposed alternative method of execution, the severity and duration of pain likely to be produced, and how they compare to the state's method of execution."
Bucklew's lawyers said the court should clarify that inmates "need not custom-design their own method of execution in light of the idiosyncratic reasons the state's generally lawful method of execution will prove cruel as applied to them."
The case is Bucklew v. Precythe