We already have. The old regime is dead.
Actually, we just put the "old regime" in charge of Fallujah.
Saddam Hussein al-Tikriti is most certainly not dead (although we should have killed him), and if we don't, there is a chance that he will be back in power.
Like Napoleon, there will be a moment when he throws open his cloak and says, "Soldiers of Iraq-shoot me if you must!"
I don't think they will.
Oops! One of the old regime's generals was just resurrected and we have turned Fallujah over to him!