Death penalty is barbaric but these methods are just cruel. Why not use preferred methods for euthanasia, like exit bag? It's fast, painless and cheap.
It covers this quite nicely - Includes an interview with a death penalty advocate and asks about a 'theoretical painless execution method' and the advocate agrees that if such thing were available it would be ideal.
Then later, after Portillo has done a bunch of investigation, hypoxia (I think) is landed on as an ideal solution. It's put to the advocate, who then squirms and insists that it's not a suitable 'punishment'.
My memory is hazy since I haven't seen it in a decade, but it's a fantastic doco and probably freely available now.