Newly minted justice Brett Kavanaugh heard oral arguments Tuesday morning in his first death penalty case, a controversial subject that is almost perpetually before the High Court.

The case, Bucklew v. Precythe, is the latest of many appeals by multiple murderer Russell Bucklew to delay his execution—he was convicted and sentenced to death more than 20 years ago. This latest appeal (called an "as applied" challenge) is concerned with the method of execution used by the state of Missouri as applied to Bucklew but represents yet another instance of the Supreme Court's justices being forced to grapple with the strange contours of lethal injection.

Bucklew suffers from a rare disease called cavernous hemangioma, which "has caused unstable, blood-filled tumors to grow in his head, neck, and throat." These tumors are known to burst, causing Bucklew’s airways to be flooded. He argues there is a very real risk that while undergoing lethal injection, one will burst, causing him to effectively drown on the table, a fate he contends violates the Eighth Amendment's prohibition on cruel and unusual punishment.

Citing this, Bucklew is seeking an alternative form of execution: nitrogen gas hypoxia, which is broadly embraced by proponents of voluntary euthanasia as a mechanism for painless suicide. Although the gas chamber is authorized as an alternative form of execution in Missouri, the state argues that this has historically meant execution with cyanide gas.

The questions presented by the Court in Bucklew are actually a little more complicated even than this. Specifically, they concern how and whether or not Bucklew presented his alternative means of execution—a very important question since 2015's Glossip v. Gross, the highly controversial case that found lethal injection is permissible under the Eighth Amendment but also gave capital convicts the right to propose an alternative method of execution, assuming they met certain thresholds.

If the preceding sounds confusing, that is because it is. Bucklew is the latest in a series of cases which concern themselves with the contours of what does and does not constitute "cruel and unusual punishment" as far as the death penalty is concerned. The Court has been tied up in trying to answer this question since 1972's Furman v. Georgia, when it temporarily stayed the death penalty nationwide under the stipulation that as then-implemented, it was constitutional. Capital punishment was relegalized four years later, but the Court's tricky entanglement with it has proceeded ever since.

As such, Kavanaugh's first death penalty oral argument is an important indicator of the direction of the future of the Court. The Associated Press reported that Kavanaugh focused primarily on practical questions during oral arguments: Will Bucklew be lying flat on his back during the execution? What are the limits on pain during an execution? Kavanaugh also directed most of his questions at counsel for the state of Missouri, which may indicate that he has more sympathy for Bucklew's side.

Kavanuagh's vote is of particular significance because, the AP noted, his predecessor Anthony Kennedy was the deciding vote in granting Bucklew a reprieve from execution earlier this year. A final decision in Bucklew v. Precythe is expected in the spring.