We performed a series of experiments examining the effect of contrast on the perception of moving plaids. This was done to test the hypothesis put forth by Adelson and Movshon (1982) that the human visual system determines the direction of a moving plaid in a two-staged process: decomposition into component motion followed by application of the intersection of constraints rule. Although there is recent evidence that the first tenet of their hypothesis is correct, i.e. that plaid motion is initially decomposed into the motion of the individual grating components (Movshon, Adelson, Gizzi & Newsome, 1986; Welch, 1989), the nature of the second-stage combination rule has not as yet been established. We found that when the gratings within the plaid are of different contrast, the perceived direction is not predicted by the intersection of constraints rule. There is a strong (up to 20 deg) bias in the direction of the higher-contrast grating. A revised model, which incorporates a contrast-dependent weighting of perceived grating speed as observed for 1-D patterns (Thompson, 1982), can quantitatively predict most of our results. We discuss our results in the context of various models of human visual motion processing and of physiological responses of neurons in the primate visual system.