The Supreme Court, its conservative majority in place for years, no longer debates whether state-imposed death is morally right or constitutionally valid. Justice Brett Kavanaugh’s confirmation last month all but guarantees this will remain true for another generation, despite Justice Stephen Breyer’s best efforts. Since the court doesn’t weigh the substance of the death penalty, it instead focuses on the aesthetics of the system it oversees.

These aesthetics are vital to maintaining public support for the system. American capital punishment is ritualized, with a carefully orchestrated set of appeals that often culminates in a last-minute denial from the Supreme Court. It’s also theatrical: Executions are choreographed to produce a quiet spectacle for an audience of witnesses, who then convey what they see to the wider world. Justice Harry Blackmun, concluding in 1994 that the system no longer met constitutional standards, described it as “the machinery of death.”

The court’s docket this term shows how much that machinery has deteriorated since then, and raises questions about how long the justices can uphold capital punishment while Americans increasingly lose faith in it.

The court first heard oral arguments on Tuesday in Bucklew v. Precythe, an unusual lethal-injection case. A Missouri jury sentenced Russell Bucklew to death in 1998 for murdering a man he found with his ex-girlfriend, whom Bucklew then kidnapped and raped. Bucklew does not challenge the validity of his sentence or any of the procedural aspects surrounding it. Instead, he’s challenging the manner in which Missouri seeks to end his life.

Bucklew suffers from a gruesome condition known as cavernous hemangioma, which creates malformations in some of the body’s blood vessels. Over time, those malformations swell and fill with blood until they form benign tumors. The rare condition can manifest anywhere on the body. Bucklew’s case is even more unusual because it primarily affects his mouth and throat. His uvula is covered in blood-filled tumors that make it harder to eat, breathe, and sleep. There is no cure for the condition, and it will progressively worsen for as long as he lives.