Death Penalty- Revenge or Justice?

This is a very contentious issue so much so that I believe that European Union first demand from aspirant member countries is to abolish the death penalty as they think that it is cruel and inhumane punishment. Same thing goes with Amnesty International in London who clamor to get the remaining countries of the world where it is widely practiced to abolish it. Here in America it is used disproportionately more by some southern states than northern states. Amnesty keeps on reminding the world that the U.S. is one of the few industrialized countries where it is an acceptable form of punishment and despite massive efforts by the Amnesty, they have not been able to stop this practice. Even human right groups clamor to stop this punishment once and for all and replace it by some form of life punishment. Now here is where I differ with Amnesty International and European Union and all the death penalty opponents. Is it ever appropriate to apply death penalty in any case. I can understand that sometimes wrong person is put to death and that is a tragedy and it should never happen. We should make sure beyond doubt that the person being convicted of Death penalty deserves it after all evidence points to him/her. But what if all evidence leads to the person that did the crime, does he not deserve to die. That is again the same hotly debated question which is being going on for years and will be for many years to come.