We have shown previously that random dots with an interocular time delay (ITD), the time difference of the onset of dots between the two eyes, yield both apparent depth and motion, although depth and velocity are covariant and, thus, ITD is inherently ambiguous. The depth of random dots with ITD was proportional to ITD, suggesting that the visual system assumes a constant velocity of the dots and determines depth on the basis of this constant velocity. We performed psychophysical experiments to investigate whether subjects perceive a constant velocity with a variety of ITDs in random dots aligned along a single vertical line that ensures neither apparent motion nor accidental disparity between the dots. The results showed that subjects perceive a constant velocity for a variety of ITDs with simultaneous perception of depth in proportion to ITD, indicating the priority of depth over velocity in ambiguous binocular perception derived from ITD. (C) 2011 Optical Society of America