All 12 jurors agreed to convict Kenneth Eugene Smith in the 1988 murder of a pastor’s wife in Alabama, but when it came time to recommend a sentence, 11 of them voted to spare him and instead send him to prison for life.

But the judge overruled the jury and sentenced Mr. Smith to death, a practice that Alabama banned in 2017 and that is no longer allowed anywhere in the United States. That ban did not apply to prior cases, however, and the state now plans to execute Mr. Smith, 57, on Thursday evening at a prison in southwest Alabama.

The Supreme Court on Wednesday rejected a request by Mr. Smith’s lawyers to halt the execution, which was scheduled to proceed Thursday evening.

Mr. Smith was convicted in 1996 of murdering Elizabeth Dorlene Sennett, the wife of a pastor, after her husband arranged to pay him and another man $1,000 each to kill her. The husband killed himself a week after the murder, and the other hired hit man was executed in 2010.

At his sentencing proceeding, Mr. Smith’s lawyers noted that he was 22 years old at the time of the crime and had been “neglected and deprived” in his childhood. Other mitigating factors included that Mr. Smith was remorseful, had no significant criminal history and had conducted himself well in jail. Eleven jurors voted for a life sentence with no parole.

But the judge in the case, N. Pride Tompkins, said that the aggravating factors in the case outweighed those issues: Mr. Smith had been paid for the crime, and he had ample opportunity to back out of the murder-for-hire plan but went along with it anyway. Jurors, he said, had heard an “emotional appeal” from Mr. Smith’s mother. Overruling the jury, he imposed the death sentence.

Alabama is one of four states — in addition to Delaware, Florida and Indiana — that ever allowed judges to overrule jurors who recommended against a death sentence, according to the Death Penalty Information Center. All of those states have since outlawed the practice or had it declared illegal by courts.

Mr. Smith’s lawyers argued to the U.S. Supreme Court that carrying out a death sentence despite a jury recommending life in prison constituted cruel and unusual punishment.

The court did not give any reasons for its decision not to halt the execution. On Thursday, Mr. Smith’s lawyers were pursuing a series of last-minute appeals.

The execution is one of four being carried out this week across the country, in Arizona, Texas and Oklahoma.

Alabama has had problems administering lethal injections in recent months, and Thursday’s execution will be closely watched.

In July, prison officials struggled for hours to find a suitable vein in order to execute Joe Nathan James, and a private autopsy suggested that one of his arms had been cut during the process, according to court records. The problem was first reported in The Atlantic.

Prison officials ultimately killed Mr. James by lethal injection, but months later, there was a similar problem finding a suitable vein in another man, Alan Eugene Miller, leading officials to call off the execution shortly before midnight, when the death warrant was to expire.

It has not yet been rescheduled.