|Abstract:||An idempotent phonological grammar maps phonotactically licit forms faithfully to themselves. This paper establishes tight sufficient conditions for idempotency in (classical) Optimality Theory. Building on Tesar (2013), these conditions are derived in two steps. First, idempotency is shown to follow from a general formal condition on the faithfulness constraints. Second, this condition is shown to hold for a variety of faithfulness constraints which naturally arise within McCarthy and Prince?s (1995) Correspondence Theory of faithfulness. This formal analysis provides an exhaustive toolkit for modeling chain shifts, which have proven recalcitrant to a constraint-based treatment.