That was not my point. My point was that death penalty does not prevent actual criminals from murdering people. Hence, I don't see what is the point of capital punishment. Moreover, I don't think that judges and juries should have the right to play God and decide who lives or dies.
I agree with your comment about the DP not being a deterrent. People who murder people aren't thinking, "I can handle life without parole, but gee, I can't handle that death penalty!". Thoughts about consequences only begin for them after getting caught.
I'm neutral on your second point. I think there are examples of criminals with crimes that are so sick and heinous in nature to where I could see the argument that taking their life away is a just and proportional penalty.
I do think there's one thing that has to be taken into account when talking about the DP, though: it seems to be a powerful bargaining chip. Here's a paper from earlier this year that finds criminals are significantly more likely to plea to life or long sentences in states where they may face the DP compared to states where they will not: http://www.cjlf.org/papers/wpaper09-01.pdf
There are papers, though, which make arguments that come to different conclusions. This is well outside of my area of knowledge, but my point in bringing it up is to identify it as another thing that bears consideration in the DP discussion.
What do you suggest in order to deter an innocent man from committing the crime that he never committed?