The petitioners’ lawyers will doubtless seek stays. In Mr. Glossip’s case, they will have to act quickly.

How the court responds will illuminate the current vitality of its fitful commitment to a procedure it sometimes uses to bridge the voting gap: the “courtesy fifth” vote to stay executions. Such votes are said to be available once the court makes a formal decision to grant review of a condemned prisoner’s case.

Justice Lewis F. Powell explained his reluctant decision to cast such a courtesy vote in a 1985 concurrence. The inmate’s case had “no merit whatever,” he wrote. “But in view of the unusual situation in which four justices have voted” to hear it, he wrote, “and in view of the fact that this is a capital case with petitioner’s life at stake, and further in view of the fact that the justices are scattered geographically and unable to meet for a conference, I feel obligated to join in granting the application for a stay.”

But such a fifth vote is not always forthcoming. In the late 1980s, the question of when courtesy votes were warranted was a source of tension on the court, and by 1990 the consensus broke down entirely.

“For the first time in recent memory,” Justice William J. Brennan Jr. wrote in a dissent that year, “a man will be executed after the court has decided to hear his claim.”

Thomas C. Goldstein, the publisher of Scotusblog, has written that a courtesy fifth has been uniformly available since the later part of the tenure of Chief Justice William H. Rehnquist, who served from 1986 to 2005. If there are four votes formally to grant review, Mr. Goldstein wrote, a courtesy fifth vote for a stay will always materialize.