Price level targeting has been proposed as an alternative to inﬂation targeting that may confer beneﬁts if a central bank sets policy under discretion, even if societyu0092s loss function is speciﬁed in terms of inﬂation (instead of price level) volatility. This paper demonstrates the sensitivity of this argument. If even a small portion of agents use a rule-of-thumb to form inﬂation expectations, or does not fully understand the nature of the target, price level targeting may in fact impose costs on society rather than beneﬁts. While rational expectations and perfect credibility are generally beneﬁcial with either a price level or an inﬂation target, an inﬂation target is more robust to alternative assumptions. These results suggest that caution should be exercised in considering a price level target as the basis for monetary policy, unless society has preferences speciﬁed in terms of price level, rather than inﬂation, volatility.