Abstract Both price level targeting and speed limit policies have been suggested as alternatives to inflation targeting that may confer benefits when a central bank operates under discretion, even if society’s loss function is specified in terms of inflation volatility. Here we show that price level targeting dominates a speed limit policy under perfect credibility and rational expectations. However, a speed limit policy is more robust than a price level target. Even for small deviations from either rational expectations or perfect credibility, a speed limit policy dominates a price level target.