We determine optimal discretionary monetary policy in a New-Keynesian model when nominal interest rates are bounded below by zero. Nominal interest rates should be lowered faster in response to adverse shocks than in the case without bound. Such ‘preemptive easing’ is optimal because expectations of a possibly binding bound in the future amplify the effects of adverse shocks. Calibrating the model to the U.S. economy we ?nd the easing effect to be quantitatively important. Moreover, signi?cant welfare losses. Losses increase further when in?ation is partly determined by lagged in?ation in the Phillips curve. Targeting positive in?ation rates reduces the frequency of a binding lower bound, but tends to reduce welfare compared to a target rate of zero. The welfare gains from policy commitment, however, appear signi?cant and are much larger than in the case without lower bound.