When we grasp with one eye covered, the finger and thumb are typically opened wider than for binocularly guided grasps, as if to build a margin-for-error into the movement. Also, patients with visual form agnosia can have profound deficits in their (otherwise relatively normal) grasping when binocular information is removed. One interpretation of these findings is that there is a functional specialism for binocular vision in the control of grasping. Alternatively, cue-integration theory suggests that binocular and monocular depth cues are combined in the control of grasping, and so impaired performance reflects not the loss of ‘critical’ binocular cues, but increased uncertainty per se. Unfortunately, removing binocular information confounds removing particular (binocular) depth cues with an overall reduction in the available information, and so such experiments cannot distinguish between these alternatives. We measured the effects on visually open-loop grasping of selectively removing monocular (texture) or binocular depth cues. To allow meaningful comparisons, we made psychophysical measurements of the uncertainty in size estimates in each case, so that the informativeness of binocular and monocular cues was known in each condition. Consistent with cue-integration theory, removing either binocular or monocular cues resulted in similar increases in grip apertures. In a separate experiment, we also confirmed that changes in uncertainty per se (keeping the same depth cues available) resulted in larger grip apertures. Overall, changes in the margin-for-error in grasping movements were determined by the uncertainty in size estimates and not by the presence or absence of particular depth cues. Our data therefore argue against a binocular specialism for grasp programming. Instead, grip apertures were smaller when binocular and monocular cues were available than with either cue alone, providing strong evidence that the visuo-motor system exploits the redundancy available in multiple sources of information, and integrates binocular and monocular cues to improve grasping performance.