Yoking the movement of the stimulus on the screen to the movement of the head, we examined visual stability and depth perception as a function of head-movement velocity and parallax. In experiment 1, for different head velocities, observers adjusted the parallax to find (a) the depth threshold and (b) the concomitant-motion threshold. Between these thresholds, depth was seen with no perceived motion. In experiment 2, for different head velocities, observers adjusted the parallax to produce the same perceived depth. A slower head movement required a greater parallax to produce the same perceived depth as faster head movements. In experiment 3, observers reported the perceived depth for different parallax magnitudes. Perceived depth covaried with smaller parallax without motion perception, but began to decrease with larger parallax and concomitant motion was seen. Only motion was seen with the larger parallax.