This paper compares a monetary policy that targets average inflation with one that targets the change in the output gap. It shows that the stabilizing properties of monetary policy strategies are sensitive to both the existence of lags in the transmission mechanism and the design of target rules. A strategy focusing on the change in the output gap is likely to prove inferior to targeting the average rate of inflation in a model where monetary policy affects the real economy sooner than inflation. Even more favourable results for average inflation targeting emerge in a framework that also includes forward-looking expectations. These results stand in marked contrast to those in standard models where policy lags are absent. To ensure sound choice of policy, central banks are advised to examine the stabilizing properties of monetary policies in a variety of models.