In Optimality Theory, constraints come in two types, which are distinguished by their mode of evaluation. Categorical constraints are either satisfied or not; a categorical constraint assigns no more than one violation-mark, unless there are several violating structures in the form under evaluation. Gradient constraints evaluate extent of deviation; they can assign multiple marks even when there is just a single instance of the non-conforming structure. This article proposes a restrictive definition of what an OT constraint is, from which it follows that all constraints must be categorical. The various gradient constraints that have been proposed are examined, and it is argued that none is necessary and many have undesirable consequences.