This paper considers the desirability of the observed tendency of central banks to adjust interest rates only gradually in response to changes in economic conditions. It shows, in the context of a simple model of optimizing private-sector behavior, that such inertial behavior on the part of the central bank may indeed be optimal, in the sense of minimizing a loss function that penalizes inflation variations, deviations of output from potential, and interest-rate variability. Sluggish adjustment characterizes an optimal policy commitment, even though no such inertia would be present in the case of a reputationless (Markovian) equilibrium under discretion. Optimal interest-rate feedback rules are also characterized, and shown to involve substantial positive coefficients on lagged interest rates. This provides a theoretical explanation for the numerical results obtained by Rotemberg and Woodford (1998) in their quantitative model of the U.S. economy.