As death penalty opponents have noted, there is no clean, painless or humane way to kill a person. Even with modern drug cocktails designed to bring a swift painless death by lethal injection, things often go awry.
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Still, some methods of execution are faster and cleaner than others. Foley's captors didn't just want to kill him, they wanted to kill him in a most gruesome way and record it as a warning. There are far less gruesome ways to kill a person, but few things make a greater impression on the public than seeing a severed head. The goal is to instill fear and send a message that they mean business, and that their demands must be met.
One need not travel to the Middle East to find the practice of beheading. In fact the United States shares a border with a country where dozens of people have been decapitated in just the past few years. Mexican criminal organizations including the drug gang Zeta routinely decapitate and dismember their victims. Headless bodies are sometimes found hanging from public places, including highway overpasses and bridges. Sometimes their hands or feet are cut off as well. Just last year four women caught up in the drug wars were killed by masked gunmen. Not only were they beheaded, but their killing was recorded on videotape and made available online, just as Foley's murder was.