It is shown how the full three-dimensional structure of a scene may in principle be computed from a correlated pair of retinal images, when all that is known about the orientations of the two eyes is that the planes of their horizontal meridians accurately coincide. The vertical dimension plays a crucial role in the theory; visible points which lie on the horizontal meridian supply no information about the angle of convergence or the direction of gaze. (i) If the scene contains three or more nonmeridional points, not all lying in a vertical plane, then their positions in space are fully determined by the horizontal and vertical coordinates of their images on the two retinas. (ii) If just two nonmeridional points are visible, or more than two, lying in a vertical plane, then their retinal images admit, in general, just two distinct three-dimensional interpretations. One of these is usually unrealistic; but a choice between them may be perceptually difficult if the vertical plane containing the points is nearly perpendicular to the interocular axis. These results suggest that vertical disparities may play an important role in the binocular perception of absolute depth. Elsewhere (Mayhew, this issue) this suggestion is found to provide a quantitative explanation of Ogle's 'induced effect'.