If any person manages to develop a way to completely eliminate government (yeah, I accidentally typed that first. Freudian slip?) corruption while still retaining a functioning system, a new Nobel prize should be created just for them, for "Winning Life". Get it? Because it isn't going to happen. Perhaps it is the semisuicidal cynic in me talking, but all forms of government are corrupt, just in different ways. The trick is in finding a type and balance of corruption, greed and general bastardism that doesn't impact your own life too badly, because there isn't a snowball's chance in the center of a supernova of having a lasting system that is entirely free of corruption.
I think their would be very little corruption, waste or ineptitude in a government limited only to its very basic functions of maintaining rule of law. Police, military, courts, maybe environmental protection not much else. A government constitutionally defined by what it is
permitted to do and not one defined by what it cannot do. Since the government isn't legally allowed to do anything besides wage war and arrest for serious crimes, there just would not be any reason to give any public official money or vice versa, since no official could possibly create or enforce any policy that could effect anything outside the limited scope of national defense and public security. People are awful and far from perfect, but if you take away their power they can't do much harm, you know?
Of course, that's just social-Darwinism and such a society would arguably be pretty backwards without public education and nothing but toll-roads everywhere. So I guess there is a price to pay to live in a society like this, since you have to trust a large government with far-reaching powers to do the right thing, since no other organization or group of organizations can.