All federal systems face the two fundamental dilemmas of federalism: too strong a center risks overawing the subnational units; and too weak a center risks free-riding that makes the system fall apart. Resolving the two dilemmas is problematic because mitigating one dilemma exacerbates the other. We develop a model of federal institutions that shows the circumstances under which both dilemmas can be solved so that federal institutions are self-enforcing.