How does the human visual system compute the speed of a coherent motion stimulus that contains motion energy in different spatiotemporal frequency bands? Here we propose that perceived speed is the result of optimal integration of speed information from independent spatiotemporal frequency tuned channels. We formalize this hypothesis with a Bayesian observer model that treats the channel activity as independent cues, which are optimally combined with a prior expectation for slow speeds. We test the model against behavioral data from a 2AFC speed discrimination task with which we measured subjects' perceived speed of drifting sinusoidal gratings with different contrasts and spatial frequencies, and of various combinations of these single gratings. We find that perceived speed of the combined stimuli is independent of the relative phase of the underlying grating components, and that the perceptual biases and discrimination thresholds are always smaller for the combined stimuli, supporting the cue combination hypothesis. The proposed Bayesian model fits the data well, accounting for perceptual biases and thresholds of both simple and combined stimuli. Fits are improved if we assume that the channel responses are subject to divisive normalization, which is in line with physiological evidence. Our results provide an important step toward a more complete model of visual motion perception that can predict perceived speeds for stimuli of arbitrary spatial structure.