During Scott Peterson's initial trial, there were several petitions made to the California Supreme Court. And under California law, every person sentenced to the death penalty has a constitutional right to be heard before the state supreme court.

http://www.courttv.com/trials/peters...cution_ap.html

After the California Supreme Court, it could go through the federal appeals process (all on our tab, of course).

Furthermore, some legal experts were saying that Peterson should be glad to get the death penalty because it is possibly more likely that his conviction will be overturned by the Supreme Court than if he were to just appeal to a lower appeals court. This is because capital punishment cases by law have a much higher level of scrutiny. Though I must admit that those "legal experts" have been few, and not very well known. Still the point remains: We are paying even more money to keep Peterson alive, than if we just locked him up and threw away the key.