Binocular neurons in the visual cortex are thought to form the neural substrate for stereoscopic depth perception. How are the receptive fields of these binocular neurons organized to encode the retinal position disparities that arise from binocular parallax? The conventional notion is that the two receptive fields of a binocular neuron have identical shapes, but are spatially offset from the point of retinal correspondence (zero disparity). We consider an alternative disparity-encoding scheme, in which the two receptive fields may differ in shape (or phase), but are centered at corresponding retinal locations. Using a reverse-correlation technique to obtain detailed spatiotemporal receptive-field maps, we provide support for the latter scheme. Specifically, we show that receptive-field profiles for the left and right eyes are matched for cells that are tuned to horizontal orientations of image contours. However, for neurons tuned to vertical orientations, the left and right receptive fields are predominantly dissimilar in shape. These results show that the striate cortex possesses a specialized mechanism for processing vertical contours, which carry the horizontal-disparity information needed for stereopsis. Thus, in a major modification to the traditional notion of the neural basis of stereopsis, we propose that binocular simple cells encode horizontal disparities in terms of phase at multiple spatial scales. Implications of this scheme are discussed with respect to the size-disparity correlation observed in psychophysical studies.