I am going to experiement with the d20 Modern version tonight, where if you take damage in excess of your Con stat you are put down, and have to make a damage save or be reduced to -1 hp. The damage has to be from a single hit, after modification (for example a spit gun can't do it unless its a critical on one of the rolls). Given that its down to -1 rather than dead, it should mean Perps aren't killed more often (its another 9 rounds before you are dead).
We play a death save at -10 (unless instantly reduced to -10), with characters being able to linger at deaths door (to simulate the advanced medical technology of MC-1)
d20 Cthulhu has its threshold set at 10 and thats still playable.