Is the death penalty a problem for the courts or the legislature?

This is a simple question targeted toward those who understand my point and question. I am not looking for someone's two cents about whether people should or shouldn't be killed, how, or for what reason. Regardless of your stance, I am trying to get a broader perspective on how and why the Supreme Court should or should not yze the so-called "standards" of lethal injections (on a site with a much broader audience than say, Above the Law). Personally, I see it as a legislative question as opposed to a judicial one, but I'm curious as to what other lawyers or law students or legal scholars who happen to visit this site think and are willing to share.