Modern and ancient execution methods - a firing squad, electrocution, hanging, lethal gas, being burned at the stake - all made appearances during the court's sober assement of ways to kill Russell Bucklew without violating the Constitution's ban on cruel and unusual punishment.
Missouri plans to use an injection of a single drug, pentobarbital, to carry out the long-delayed execution of Bucklew. But he suffers from a congenital and 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.
The result, they contend, would be that he could choke to death on his own blood.
The Supreme Court has been considering Bucklew's fate for years. Last March, it voted 5- 4 to delay his execution and hear his new challenge, in which proposes he be killed using gas, something Missouri authorizes but has never done.
The state's lawyers say that Bucklew cannot prove his condition would cause him an abnormal amount of suffering, and that his legal fight is a ploy to further delay his punishment and open a new line of legal challenges.
Justice Anthony Kennedy was a member of the majority last spring. He has been replaced by Kavanaugh, who is considered more conservative, but who was never called upon to rule on an execution as a member of the U.S. Court of Appeals for the D.C. Circuit.
Kavanaugh directed all of his questions to Missouri State Solicitor D. John Sauer, pressing him on the outer bounds of the state's arguments.
"Are you saying even if the method creates gruesome and brutal pain you can still do it because there's no alternative?" Kavanaugh asked.
Sauer replied that under the court's previous rulings, Bucklew would have to come up with an alternative manner of execution acceptable to the state.
Kavanaugh pressed: "Is that a yes?"
Sauer replied: "Yes, it is, your honor."
Later, Kavanaugh asked whether the state had planned to make any special accomodations for Bucklew's condition, such as whether he would be lying supine on a gurney, or with his head elevated.
"Your opposing counsel said, even if everything goes according to plan, there will still be significant suffering. Can you respond to that?" Kavanaugh asked.
"I absolutely, absolutely disagree with that," Sauer said.
The court's attention to such details about the execution was warranted because of the specific nature of Bucklew's case.
He is not contesting his guilt or his sentence of death.
In 1996, Bucklew, now 50, stalked his former girlfriend Stephanie Ray to another man's trailer. He shot and killed the man, Michael Sanders, tried to shoot Ray's fleeing child and then captured Ray. He handcuffed and raped her, then wounded a police officer in a subsequent gunfight.
Bucklew later escaped from jail and attacked Ray's mother with a hammer before he was recaptured.
He also is not challenging the constitutionality of the death penalty, or even of Missouri's lethal injection procedure. His claim is that applied to his specific condition, the protocol would result in the kind of tortured death the Constitution forbids.
A divided court has upheld lethal injection against a series of challenges. And it has indicated that an inmate who makes a specific challenge specific to his condition must propose an alternative manner of execution.
Justice Sonia Sotomayor has been the court's most outspoken critic of that decision, and said Tuesday that her colleagues had "made up" that requirement without constitutional justification.
Nonetheless, she tried to narrow the impact of ruling for Bucklew.
It "is not going to abolish the death penalty with respect to everybody," she said. "It's going to tell the state: If you have an individual with a unique circumstance in which a method of execution is going to cause that person excruciating pain, cruel and unusual pain, you better find a different way."
Justice Stephen Breyer pressed Kavanaugh's point. He said all would agree that burning someone at the stake would violate the Constitution, so why wouldn't an inmate be able to challenge a method of death that had the same physical sensation for the condemned.
Conservatives Chief Justice John Roberts and Justice Samuel Alito were the toughest questioners of Bucklew's attorney, Robert Hochman of Chicago.
Alito questioned how Hochman could know that executing Bucklew with lethal gas would cause fewer problems than lethal injection.
And Roberts wondered about the defense's true intentions in proposing lethal gas.
"How can it be a reasonable alternative if it's never been used before?" Roberts asked, adding that death penalty litigation often involves challenges to untested execution protocols. "It seems to me that if you have a method that no state has ever used, that that danger is magnified."
Sauer picked up on that. The reason that inmates must be required to choose an "alternative method of execution that is readily feasible," is to avoid giving their lawyers "every incentive to engage in interminable litigation . . ."
Breyer suggested the case was not ready for a decision by the justices, that there were factual disagreements in the case that should be decided by lower courts.
And Sotomayor noted that Bucklew's condition was constantly changing.
He underwent a tracheotomy this summer, and Sotomayor asked Hochman if the tube was still in place. He said it was, and that he did not know when or if it would be removed.
"If the trach stays, it's a totally different case than if it's removed," Sotomayor said.
The case is Bucklew v. Precythe, and it could be months before the court renders a decision.