Time may be running out for Duane Buck, a death row inmate in Texas since 1997. Next week the U.S. Supreme Court will consider whether to hear Mr. Buck’s latest—and likely last—appeal. His argument largely rests on the use of damaging racial speculation during the sentencing phase of his trial. Mr. Buck’s supporters claim he is being executed because he is black. That is a stretch, given the facts of his crime, but his case does present a substantial challenge to the death penalty as it has been applied historically.

There...