Weakly support, and only in the case of premeditated homicide (or whatever the legal term is for cold-blooded murder).
In most sensible jurisdictions nowadays, the bump-up from first degree "intent to kill" murder to a death-penalty eligible murder occurs through the occurrence of aggravated circumstances in the crime as defined by statute - such as killing a police officer or being convicted of aggravated robbery, as well as murder in the same crime.
This occurred because of the difficulty of defining what "premeditated murder" is. Does it occur in a split-second or does it take a period of time? Courts are all over the place on this one.
I assumed there would be some confusion over how 'premeditated' is defined.
I don't quite agree with the idea that the question "who have you killed?" should play a part in determining whether a homicide is aggravated or not. But it is somewhat rational, so I suppose I support it.