Ambiguous stimuli with two distinct interpretations give rise to perceptual alternations between them. During prolonged viewing of transparently moving gratings, observers report periods of perceiving one grating in front of the other, alternating with periods of the reverse depth ordering. We measured the percepts' dominance times to study the effect of depth cues (wavelength, duty cycle, and speed) on the perceived depth ordering. The grating with shorter wavelength, lower duty cycle, or higher speed was perceived as being behind the other for a fraction of time larger than one half. The fraction of time spent perceiving each grating as behind changed gradually as a function of the parameters. The fraction of dominance depended on the ratio between the gratings' wavelengths, not on their absolute sizes. The wavelength ratio had a stronger effect on perceived depth than that of duty cycle or speed and could override stereoscopic disparity cues. Similar results were obtained with superimposed moving surfaces of random dots. The findings are interpreted in terms of their relation to statistical properties of natural surfaces and provide evidence that the fraction of dominance of each percept represents the likelihood that it corresponds to the true interpretation of the underlying scene.