When the United States at last abandons the abhorrent practice of capital punishment, the early years of the 21st century will stand out as a peculiar period during which otherwise reasonable people hotly debated how to kill other people while inflicting the least amount of constitutionally acceptable pain.

The Supreme Court stepped back into this maelstrom on Friday, when it agreed to hear Warner v. Gross, a lawsuit brought by four Oklahoma death-row inmates alleging that the state’s lethal-injection drug protocol puts them at risk of significant pain and suffering.

In accepting the case, the justices had to change its name. The lead plaintiff, Charles Warner, was executed on Jan. 15 after the court, by a vote of 5-to-4, denied him a last-minute stay. That may sound strange until you consider that while it takes only four justices to accept a case for argument, it takes five to stay an execution. The case is now named for another inmate, Richard Glossip. (On Monday, the Oklahoma attorney general requested temporary stays of the impending executions of Mr. Glossip and the other two plaintiffs.)

Mr. Warner was sentenced to death for raping and murdering an 11-month-old girl named Adrianna Waller in 1997. His execution was originally scheduled for last April, but it was postponed when officials botched the execution directly before his — leaving the inmate, Clayton Lockett, writhing and moaning on the killing table for more than half an hour. The plaintiffs in the current case challenge the continued use of one of the drugs that may have contributed to Mr. Lockett’s prolonged death, the sedative midazolam.