Recent work has shown that the ability of moving contour terminators to determine the perceived motion of untextured contours is strongly constrained by whether contour terminators are classified as intrinsic (belonging to a moving contour) or extrinsic (belonging to a surface occluding a moving contour). It has also been demonstrated that stereopsis can play a decisive role in this classification. Specifically, Shimojo, Silverman and Nakayama (1989, Vision Research 29, 619-626) argued that the efficacy of stereopsis in classifying moving contour terminators as intrinsic or extrinsic stemmed from the relative depth relationships specified by binocular disparity. Here, evidence is presented which demonstrates that the visual system relies on the presence of unpaired contour terminators to classify stereoscopic contour terminators as extrinsic. The author shows that the tendency to perceive untextured contours translating in a single rectangular aperture in a direction parallel to the longer axis of the aperture (the barberpole illusion) was not abolished by stereoscopic depth differences when the contour terminators were interocularly paired. However, the illusion was abolished when the contours terminators along the longer axis of the aperture were interocularly unpaired. Moreover, contours translated within a square aperture revealed a systematic shift towards the direction of motion signaled by the binocularly paired contour terminators along the horizontal edges of the aperture. These results demonstrate that the classification of stereoscopic contour terminators along an extrinsic-intrinsic dimension results from the presence of local, unpaired contour terminators rather than the relative depth or disparity differences per se, or via the global integration of contour terminators across multiple apertures when multiple apertures are present.