The paper investigates the computational complexity of different versions of Optimality Theory (OT). The result of Frank and Satta (1998) is used as a starting point. These authors show that unidirectional optimization can be implemented by finite state techniques if only binary constraints are used. The consequences of (a) taking gradient constraints into account and (b) using bidirectional optimization in the sense of Blutner (2000) are explored. The central result of the paper is that the combination of gradient constraints and bidirectionality leads to a massive increase of computational complexity.