How do humans perceive the speed of a coherent motion stimulus that contains motion energy in multiple spatiotemporal frequency bands? Here we tested the idea that perceived speed is the result of an integration process that optimally com- bines speed information across independent spatiotemporal frequency channels. We formalized this hypothesis with a Bayesian observer model that combines the likelihood functions provided by the individual channel responses (cues). We ex- perimentally validated the model with a 2AFC speed discrimination experiment that measured subjects’ perceived speed of drifting sinusoidal gratings with differ- ent contrasts and spatial frequencies, and of various combinations of these single gratings. We found that the perceived speeds of the combined stimuli are inde- pendent of the relative phase of the underlying grating components. The results also show that the discrimination thresholds are smaller for the combined stimuli than for the individual grating components, supporting the cue combination hy- pothesis. The proposed Bayesian model fits the data well, accounting for the full psychometric functions of both simple and combined stimuli. Fits are improved if we assume that the channel responses are subject to divisive normalization. Our results provide an important step toward a more complete model of visual mo- tion perception that can predict perceived speeds for coherent motion stimuli of arbitrary spatial structure.