It has been established that the motion in depth of stimuli visible to both eyes may be signalled binocularly either by a change of disparity over time or by the difference in the velocity of the images projected on each retina, known as an interocular velocity difference. A two-interval forced-choice stereomotion speed discrimination experiment was performed on four participants to ascertain the relative speed of a persistent random dot stereogram (RDS) and a dynamic RDS undergoing directly approaching or receding motion in depth. While the persistent RDS pattern involved identical dot patterns translating in opposite directions in each eye, and hence included both changing disparity and interocular velocity difference cues, the dynamic RDS pattern (which contains no coherent monocular motion signals) specified motion in depth through changing disparity, but no motion through interocular velocity difference. Despite an interocular velocity difference speed signal of zero motion in depth, the dynamic RDS stimulus appeared to move more rapidly. These observations are consistent with a scheme in which cues that rely on coherent monocular motion signals (such as looming and the interocular velocity difference cue) are less influential in dynamic stimuli due to their lack of reliability (i.e., increased noise). While dynamic RDS stimuli may be relatively unaffected by the contributions of such cues when they signal that the stimulus did not move in depth, the persistent RDS stimulus may retain a significant and conflicting contribution from the looming cue, resulting in a lower perceived speed.