We show that the initial ocular following responses elicited by motion of a large pattern are modestly attenuated when that pattern is shifted out of the plane of fixation by altering its binocular disparity. If the motion is applied to only restricted regions of the pattern, however, then altering the disparity of those regions severely attenuates their ability to generate ocular following. This sensitivity of the ocular tracking mechanism to local binocular disparity would help the observer who moves through a cluttered 3-D world to stabilize objects in the plane of fixation and ignore all others.