When two drifting cosine gratings are superimposed, they will, under appropriate conditions, form a coherently moving two-dimensional pattern whose resultant direction of motion may either be between (type I), or outside (type II) the directions of the two components. We have previously shown that type I patterns produce much stronger masking than either of their components, while type II patterns do not. In this study, we measured perceived direction of motion and thresholds for discrimination of motion direction. We found that type II patterns had a perceived bias of about 7.5 deg toward the direction of their components, and had discrimination thresholds around 6.5 deg, whereas type I patterns had discrimination thresholds around 1.0 deg and no significant bias. We conclude that the neural mechanisms which compute two-dimensional image motion do not strictly implement the intersection-of-constraints construction proposed by Adelson and Movshon (1982).