BeverlyAnn, the problem is that the death penalty in that case is not a deterrent, because most crimes are not premeditated first, and criminals never think they'll be caught, second. (I've much more studies on the side of non deterrence than the other side, and the real life example of most democracies shows that this is the case).
So, you're left with revenge and retribution as the main reason for the death penalty, which is I guess fine if that's stated up front (instead of thinking it will prevent crime). The main problem then is making sure you've got the right person, you're not executing the wrong person in the thirst for revenge.
Right now, with the state of the legal system in response to poorer individuals, especially minorities, no such assurance can be given.
So, your left with the option of possibly executing an innocent in a search for retribution.
If they limit executions to cases with direct physical evidence, first rate public defendants, strong oversight of the judiciaries fairness in regards to minorities and accused with marked long term psychopatic tendencies which makes their rehabilitation unlikely, then the death penalty may be the best option in a whole array of unsatisfactory options.