WASHINGTON — John Balentine was an hour away from being put to death in Texas last month when the Supreme Court granted him a stay of execution.

The unseemly and unsettling spectacle of a last-minute legal scramble in the shadow of the ultimate deadline, with the condemned inmate waiting for word of his fate just outside the death chamber, may suggest that the Supreme Court does not render considered justice when it is asked to halt an execution.

But it tries. Indeed, the court goes to extraordinary lengths to get ready, and its point person is a staff lawyer named Danny Bickell.

“Cases where there is an execution date,” he said with a sigh, “that’s where I come in.”

Mr. Bickell’s formal title is emergency applications clerk, but capital defense lawyers have an informal title for him, too. They call him the death clerk.