The role of two binocular cues to motion in depth—changing disparity (CD) and interocular velocity difference (IOVD)— was investigated by measuring stereomotion speed discrimination and static disparity discrimination performance (stereoacuity). Speed discrimination thresholds were assessed both for random dot stereograms (RDS), and for their temporally uncorrelated equivalents, dynamic random dot stereograms (DRDS), at relative disparity pedestals of –19, 0, and +19 arcmin. While RDS stimuli contain both CD and IOVD cues, DRDS stimuli carry only CD information. On average, thresholds were a factor of 1.7 higher for DRDS than for RDS stimuli with no clear effect of relative disparity pedestal. Results were similar for approaching and receding targets. Variations in stimulus duration had no significant effect on thresholds, and there was no observed correlation between stimulus displacement and perceived speed, confirming that subjects responded to stimulus speed in each condition. Stereoacuity was equally good for our RDS and DRDS stimuli, showing that the difference in stereomotion speed discrimination performance for these stimuli was not due to any difference in the precision of the disparity cue. In addition, when we altered stereomotion stimulus trajectory by independently manipulating the speeds and directions of its monocular half-images, perceived stereomotion speed remained accurate. This finding is inconsistent with response strategies based on properties of either monocular half-image motion, or any ad hoc combination of the monocular speeds. We conclude that although subjects are able to discriminate stereomotion speed reliably on the basis of CD information alone, IOVD provides a precise additional cue to stereomotion speed perception.