The tendency for changes in the federal funds rate to be implemented gradually has been considered evidence of an interest-rate smoothing objective for the Federal Reserve. This paper investigates whether gradual movements in the federal funds rate can be explained by the dynamic structure of the economy and the uncertainty that the Fed faces regarding this structure, without recourse to including an ad-hoc interest rate smoothing argument in the objective function of the Fed. The analysis calculates the optimal funds rate policy given the structural form of the economy estimated in a VAR. In the absence of parameter uncertainty, the calculated policy responds more aggressively to changes in the economy than the observed policy, resulting in a substantially higher volatility of the funds rate than observed. Parameter uncertainty, however, limits the willingness of the Fed to deviate from the policy rule that has been previously implemented. Because the Fed has historically smoothed interest rates, the calculated policy under parameter uncertainty can account for a considerable portion of the gradualism observed in funds rate movements.