Nelson has been on death row for two decades
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The US Supreme Court has ruled that a death row inmate can pursue an appeal on the grounds that lethal injection would be cruel and unusual punishment.
David Larry Nelson says his veins - damaged by drug use - make it impossible to inject him without cutting deep into his flesh and muscle.
His appeal has prompted other inmates to challenge this method of execution.
Nelson was less than three hours from execution last year when the Supreme Court gave him a temporary reprieve.
He has been on death row since 1982, when he was convicted of a double murder in Alabama.
Critics
In a unanimous ruling, the court said Nelson should be allowed to argue that unless special precautions were taken, his execution would be unconstitutionally harsh.
Lethal injection was designed as a more humane execution method
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The US constitution bans "cruel and unusual" punishment.
Doctors had testified that a lethal injection may cause Nelson to suffer and haemorrhage and heart problems before the drugs kill him.
One of his lawyers told AP news agency the ruling should encourage critics of the method.
"I'd like to think maybe this is the first step in changing the way we do things," the lawyer said.
Many US states use lethal injections because they regard them as a more humane method of execution.
Alabama replaced the electric chair with lethal injections in 2002.