In recent years, many countries have successfully reduced their inflation rates to relatively low levels of 2 to 3 percent. The question then arises as to whether it would be desirable to move to even lower rates of inflation. The paper examines the benefits and costs of moving from low inflation to even lower inflation by drawing together recent work on this issue. Once a country has decided to move to an even lower rate of inflation, the question then becomes whether it would be better to achieve this objective through inflation targeting or price-level targeting. The paper critically reviews the arguments for both approaches.