In a wide variety of international macroeconomic models monetary policy cooperation is optimal, non-cooperative policies are inefficient, but optimal policies can be attained non-cooperatively by optimal design of domestic institutions/contracts. We show that given endogenous institutional design, inefficiencies of non-cooperation cannot and will not be eliminated. We model the delegation stage explicitly and show that subgame perfect, credible contracts (chosen by governments based on individual rationality) are non-zero, but are different from optimal contracts and hence lead to inefficient equilibria. Optimal contracts require cooperation at the delegation stage, which is inconsistent with the advocated non-cooperative nature of the solution. A general solution method for credible contracts and an example from international monetary policy cooperation are considered. Our results feature delegation as an equilibrium phenomenon, explain inefficiencies of existing delegation schemes and hint to a potentially stronger role for supranational authorities in international policy coordination.