Lawyers for Billy Joe Magwood want to argue that Alabama law was changed to make Magwood's crime a capital offense after it had already been committed.

Defendants aren't allowed to appeal using arguments that could have been brought in the original case, but Magwood's lawyers say that since he was sentenced to die a second time, he should be able to use a new argument in his second round of appeals.

"If it's the second time around, then it's just barred," Justice Anthony Kennedy said.

"Well, it shouldn't be barred. Because it's a new judgment, the defendant should be able to get relief the second time around," said Jeffrey L. Fisher, Magwood's lawyer.

Magwood, 58, has been on Death Row since 1981 for the shooting death of Coffee County Sheriff Neil Grantham in 1979. He got that death sentence thrown out, but then was resentenced to death.