We develop a framework that explains the choice of institutions to address international cooperation problems. We begin with boundedly rational actors who make institutional choices based on the properties of the cooperation problem they face and the menu of international institutions available to them. If the institutional status quo offers an appropriate venue for the prevailing cooperation problem, then actors will either use a focal institution or select a readily available alternative; if no suitable venue is available in the institutional status quo then costlier and riskier strategies of institutional change and creation will be pursued. The framework further allows us to incorporate the impact of international organizations and governance arrangements on the menu for institutional choice, to combine elements of rationalist and constructivist institutional accounts, and to address distributional and power considerations inherent to the choice of international institutions. The paper contains many empirical illustrations and is followed by a companion paper that applies the framework to the ongoing development of international institutions for financial reporting.