This paper investigates the theoretical implications of targeting average inflation or following a speed limit policy in a dynamic backward-looking model where monetary policy works with lags. Our findings reveal that the target horizon for expected inflation in the target rule must be correctly specified for the monetary policy strategies to achieve best results. Average inflation targeting dominates a speed limit policy for plausible values of society's relative aversion to inflation variability. The efficiency loss associated with average inflation targeting relative to optimal policy is very small if society values output stability. A speed limit policy becomes attractive only if society places great emphasis on inflation stability.