In this paper, we discuss some formal properties of the model of bidirectional Optimality Theory that was developed in Blutner 2000. We investigate the conditions under which bidirectional optimization is a well-defined notion, and we give a conceptually simpler reformulation of Blutner's definition. In the second part of the paper, we show that bidirectional optimization can be modeled by means of finite state techniques. There we rely heavily on the related work of Frank and Satta 1998 about unidirectional optimization.