Accuracy in discriminating rigid from nonrigid motion was investigated for orthographic projections of three-dimensional rotating objects. In 3 experiments the hypothesis that magnitudes of angular velocity are misperceived in the kinetic depth effect was tested, and in 4 other experiments the hypothesis that misperceiving angular velocities leads to misperceiving rigidity was tested. The principal findings were (a) the magnitude of perceived angular velocity is derived heuristically as a function of a property of the first-order optic flow called deformation and (b) perceptual performance in discriminating rigid from nonrigid motion is accurate in cases when the variability of the deformations of the individual triplets of points of the stimulus displays favors this interpretation and not accurate in other cases.