After a three-hour delay as Georgia prison officials waited for the United States Supreme Court to rule on last-ditch appeals, Robert Wayne Holsey was executed by lethal injection on Tuesday night.

Earlier on Tuesday, the Georgia Supreme Court rejected the argument by Mr. Holsey’s lawyers that the state’s unusually strict standard for judging mental disability violated the Constitution.

The lawyers immediately appealed to the Supreme Court in Washington for a stay. But in a terse note issued some 45 minutes later than the originally scheduled execution time of 7 p.m., the court said the petition, based on the claim about Georgia’s disability standard, had been denied. Justices Stephen G. Breyer and Sonia Sotomayor would have granted the request, the notice said.

The defense lawyers then filed an unusual second request for a delay, which the Supreme Court turned down around 10 p.m., allowing the lethal injection procedure to commence.