Incarceration will need to be radically modified.
Basically, any armed agression towards another individual results in the death penality, and happens quickly. Since the societal goal is to reduce the population, mistakes will be tolerated in exchange for faster resolution. Perhaps a period of 3-12 months unless its undeniable. e.g. Who started a fight could take awhile to resolve, but a mass shooter is executated almost immediately. Something will need to be done to avoid fraud so that three people can't purjure themselves and have someone exectuted. Of course, in that example, if they did, and they were caught, they too would be executed.
All other crimes against victims are settled via restitution.
Lots of grey zone here, but the default should be the death penality. For instance, I drunk driver who kills someone dies. Period.
Bottom line: People will need to become much more responsible for their actions.
"Cruel and unusual" clauses will need to be clarified in cases of the state putting someone to death. Personally, something like the gullotine, although messy, is at least absolute. Suffering, for a matter of minutes, when your guilty of killing someone else, will be acceptable. So hanging (easy to do), or drowning, or other relatively quick methods might be used.