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Is Optimality Theory a constraining theory? A formal analysis shows that it is, if two auxiliary assumptions are made: (1) that only markedness and faithfulness constraints are allowed, and (2) that input and output representations are made from the same elements. Such OT grammars turn out to be incapable of computing circular or infinite chain shifts. These theoretical predictions are borne out by a wide range of natural phonological processes including augmentation, alternations with zero, metathesis, and exchange rules. The results confirm, extend, and account for the observations of Anderson & Browne (1973) on exchange rules in phonology and morphology.