When flickering dots are superimposed onto a drifting grating, the dots appear to move coherently with the grating. In this study we examine: (i) how the perceived direction of a compound stimulus composed of superimposed grating and dots, moving in opposite directions with equal speeds, is influenced by the relative strength of the motion signals; (ii) how the perceived speed of a compound stimulus composed of superimposed grating and dots, moving in the same direction but at different speeds, is influenced by the relative strength of the motion signals; and (iii) whether this stimulus is discriminable from its metameric speed match. Dot signal strength was manipulated by using different proportions of signal dots in noise and different dot lifetimes. Both the perceived direction and speed of these compound stimuli depended upon the relative motion-signal strengths of the grating and the dots. Those compound stimuli that appeared coherent were not discriminable from the speed-matched metameric compound stimuli. When the signals were completely integrated into a coherent compound stimulus, the local motion signals were no longer perceptually available, though both contributed to the global percept. These data strongly support a weighted-combination model where the relative weights depend on signal strength, instead of a winner-takes-all model.