Should unemployment compensation be paid indefinitely at a fixed rate, or should it decline (or increase) over a worker's unemployment spell? We examine these issues using an equilibrium model of search unemployment. The model features worker-firm bargaining over wages, free entry of new jobs, and endogenous search effort among the unemployed. The main result is that an optimal insurance program implies a declining sequence of unemployment compensation over the spell of unemployment. Numerical calibrations of the model suggest that there are non-trivial welfare gains associated with switching from an optimal uniform benefit structure to an optimally differentiated system.