We calculate optimal monetary policy rules for several variants of a simple optimizing model of the monetary transmission mechanism with sticky prices and/or wages. We show that robustly optimal rules can be represented by interest-rate feedback rules that generalize the celebrated proposal of Taylor (1993). Optimal rules, however, require that the current interest rate operating target depend positively on the recent past level of the operating target, and its recent rate of increase, in a way that is characteristic of estimated central bank reaction functions, but not of Taylor's proposal. We furthermore find that a robustly optimal policy rule is almost inevitably an implicit rule that requires the central bank to use a structural model to project the economy's evolution under the contemplated policy action. However, calibrated examples suggest that optimal rules place less weight on projections of inflation or output many quarters in the future than do rules often discussed in the literature on inflation targeting, or in the current practice of inflation-forecast targeting central banks.