The spatial acuity of stereopsis is measured by presenting spatially periodic variations in binocular disparity and finding the highest spatial frequency that can be reliably detected. Although very small differences in the two eyes' images can be measured, spatial stereoacuity is much lower than the corresponding acuity for discerning luminance variations. We examined how four factors constrain stereoacuity: 1) sampling constraints imposed by the discrete nature of the random-element stereogram, 2) lowpass spatial filtering before the site of binocular combination, 3) the disparity gradient limit, and 4) the process of binocular matching. All four factors contribute. When the number of dots in the stimulus is varied, spatial stereoacuity follows Nyquist law at all but the highest dot densities. At very high densities, acuity levels off; the frequency at which it asymptotes is determined by the disparity gradient and by the spatial-frequency content of the stimulus. The way in which spatial stereoacuity behaves is quite similar to the behavior of a binocular-matching algorithm based on finding local correlations in the two eyes' images. We speculate that the binocular-matching process yields piecewise frontal estimates of the depth map and that variation in the map is constructed from those piecewise samples.