In comparison to lateral judgments of distance, stereoscopic judgments are not precise. Although stereoacuity thresholds for targets presented in the fixation plane can equal the best thresholds for the monocular hyperacuities, i.e. a few sec arc, the increment thresholds for disparity are substantially larger than the increment thresholds for lateral separation (width). We measured the minimum detectable change in the three-dimensional distance separating two features, one presented in the fixation plane, and the other some distance in front of it, i.e. with a significant standing disparity between the two features. For briefly-presented targets (150 msec), the Weber fraction for disparity was 10-20% over the range from 1 to 20 min arc, while the Weber fraction for width was only 2-3% under comparable conditions. The disparity thresholds were substantially improved for a longer duration target (1000 msec), but they were still a factor of two worse than the monocular width thresholds. In a related experiment, the vernier acuity for a standard vernier target was profoundly degraded by pairing the offset upper line presented to one eye with a disparate line in the other eye; the vernier threshold was elevated for disparities ranging from 3 to 30 min arc. This finding shows that the more precise monocular signals are actively suppressed in fused or partially-fused stereoscopic images.