Warren Lee Hill Jr., with an I.Q. of 70, is scheduled to be executed on Tuesday in Georgia. The Supreme Court should stay the execution, as his lawyers have requested, and recognize that Georgia makes it too hard for an offender to prove retardation.

In 2002, the justices banned capital punishment for the mentally retarded, but a question remains over how states handle such cases. Georgia is the only state in the country that requires a defendant to prove retardation beyond a reasonable doubt.

That is far too heavy a burden of proof because it is too easy to cast doubt on evidence concerning mental capacity.

Mr. Hill has proved his retardation in state trial court twice by the more sensible “preponderance of the evidence” standard. But the Georgia Supreme Court said Mr. Hill needed to meet the higher “beyond a reasonable doubt” standard set by state statute.