I've had this discussion with a colleague of mine before. For the two of us it came down to whether the death penalty could be applied reliably against the correct perpetrator of the crime. I argued that it could be applied with the correct amount of knowledge, and used examples of Ian Brady and Myra Hindley as examples of that. He disagreed, and believed that on this subject it is best to err on the side of caution. Yet he failed to convince me because with modern technology the perpetrator could be identified with more than enough assurance needed for such a conviction (as in ~99% certainty).
For me I am within the ~70% who believes the death penalty can be applied successfully. However I do only believe in such a measure for first degree homicide, as in that circumstance I believe that the death penalty ensures the perpetrator never again commits such a heinous act but also the punishment would fit the crime more adequately than many of the verdicts applied today.