A Deadlock-free fully adaptive routing algorithms for 2 D meshes which is optimal in the number of virtual channels reuired and in the number of restrictioins placed on the use of these virtual channels in presented. The routing algorithm improses less than half as many routing restictions as any previous fully adaptive routing algorihtm. It is also proved that, ignoring symmetry, this routing algorihm is the only fully adaptive routing algorithm that archieves both of these goals. The implementation of