A surface occluding a more distant surface gives rise to interocularly unpaired regions to its immediate left and right. The unpaired region on the left side is visible only to the left eye, whereas that on the right side is visible only to the right eye. Thus for real world scenes there are opto-geometrical constraints which determine whether particular combinations of relative depth and right-eye-only or left-eye-only stimuli are ecologically valid or invalid. We report a demonstration and experiments to show that opto-geometrically "valid" unpaired regions are seen as continuous with the rear plane and escape interocular suppression, whereas "invalid" unpaired regions are perceived as closer and are suppressed vigorously. An additional experiment indicates that the results cannot be understood in terms of correspondence solving, but require neural mechanisms that embody real-world occlusion constraints. These results suggest a rather close interaction between stereopsis and rivalry "modules". Since explicit eye-of-origin information is lost relatively early in the hierarchical organization of cortical visual processing, we argue that occlusion-related constraints must be embodied at such early levels.