Using a standard New-Keynesian model, this paper examines three reasons why monetary policy should primarily focus on price stability rather than the stabilization of output around potential, even if there appears to be an exploitable trade-off between the volatility of inflation and that of the output gap. First, we discuss the well-known time-inconsistency problem associated with active output gap stabilization. Increasing the relative weight on inflation stabilization improves the equilibrium outcome. Second, we analyse some of the problems associated with the substantial uncertainty that surrounds estimates of potential output. We argue that focusing on price stability is a robust monetary policy strategy in the face of such uncertainty. Finally, we consider the case where private agents are trying to estimate the inflation generating process using an "ad hoc", but reasonable learning rule. By emphasizing a single goal the central bank facilitates the process of learning, thereby stabilizing both inflation and the output gap.