Most computational theories of stereopsis require a registration stage prior to stereo matching to reduce the matching to a one-dimensional search. Even after registration, it is critical that the stereo matching process tolerate some degree of residual misalignment. We have studied the tolerance to vertical disparity in situations in which false targets abound and corrective eye movements are eliminated. Our main results are: vertical disparity of only the central "figure" part of a random dot stereogram can be tolerated up to about 3.5', and vertical disparity of the "figure + ground" is tolerated up to about 6.5' in the presence of monocular cues to vertical disparity. Our data suggest that this tolerance is attained by two non-motor mechanisms: the spatial average performed by the receptive fields that filter the two images prior to stereo matching, and a non-motor shift mechanism that may be driven at least in part by monocular cues.