In Latin America, as in every other part of the world, entrenched political corruption has proven to be extremely resistant to change, despite manifold efforts of legal reform and criminal prosecution. This paper proposes an explanation of this powerful resistance in terms of four interlocking vicious cycles. Once started, each cycle perpetuates itself and reinforces the other three. These vicious cycles involve (a) the informal economy, which drains income from the state treasury, (b) lack of transparency in international negotiations, (c) organized crime, which corrupts the judicial system; and (d) the patronage system of political appointments. Based on an examination of the dynamic behavior of the entire system we propose an explanation for why most reform efforts fail, and how a successful strategy can be constructed. Almost all of the insights reported in this paper were gained from the NationLab series of national strategic seminars in eight countries of Latin America.