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. We apply our approach to modern Russia where we suggest that when the center is too strong, its ability to extract rents increases and the benefits for maintaining participation in the federal bargain disappears. We also suggest strong parallels between Russia and those of the early United States under the Articles of Confederation.