DURING WEDNESDAY’S debate between GOP presidential hopefuls, Gov. Rick Perry of Texas was asked whether he “struggled to sleep at night” because of the possibility that an innocent person may have been among the 234 people executed since he took office in late 2000.

“No, sir. I’ve never struggled with that at all,” he replied. “They get a fair hearing; they go through an appellate process; they go up to the Supreme Court of the United States if that’s required.”

Henry W. Skinner can attest that sometimes not even a Supreme Court victory guarantees fairness in the state of Texas.

Mr. Skinner was convicted in 1995 of murdering his girlfriend and her two grown children. A district attorney’s office introduced physical evidence and eyewitness testimony and performed DNA tests, some of which implicated Mr. Skinner and some of which proved inconclusive. But prosecutors did not test key pieces of evidence, including a knife that appeared to have been used in one of the murders and the girlfriend’s fingernail clippings, which could contain the killer’s DNA.

In March, the Supreme Court concluded that Mr. Skinner and others like him should at least be given the opportunity to convince a court that DNA testing should be performed. With that victory in hand, Mr. Skinner’s lawyers returned to Texas to press their case in federal court. They recently filed a separate case in state court after the Texas legislature — with overwhelming bipartisan support — changed state law to make it easier for inmates to secure DNA testing.

Despite these changes and the fact that no judge has yet ruled on Mr. Skinner’s requests, the state took the extraordinary step of rescheduling his execution — for Nov. 9.

Rather than focusing on killing Mr. Skinner, prosecutors should be pushing to ensure that he receives justice. That would mean supporting his quest to test the omitted pieces of evidence. These tests could prove conclusively that he committed the crimes for which he is sentenced to die, or they could prove his innocence. We oppose the death penalty, but if it is to be carried out, it should be done with a heightened level of certainty that the person being punished is guilty. Anything short of that should cause all people of conscience to lose sleep.