It does not matter what anyone says about it: the best evidence should always be used whenever available. If there is DNA evidence, it should be used. No one should be executed if there is DNA evidence that could prove them innocent.
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According to Pat Buchannon, Gary Gilmore and the latest execution by firing squad target were Mormons, and believed that one gets to heaven quicker is killed with a spilling of blood. Perhaps this is why Utah has kept a death penalty option: for devout, but repentant, Mormons.
He also said that death by hanging was for peasants, while death by bullet was a more noble way to go.
I am not sure of the Mormon bit, but the hanging vs firing squad bit sounds likely.
Still, beheading, then drawing and quartering and sticking pieces of the executed all about the countryside, which was the way that William Wallace, who was a commoner, was dispatched, sounds pretty undignified.