Two studies of the stereopsis model of Richards were conducted using a between-subjects balanced design and a repeated trials procedure rather than the within-subjects procedure of Richards. Measures of the accuracy of discrimination between classes of retinal disparity were defined by the method of successive intervals in place of the d’ index of SDT. The results support the predictions (1) of symmetric discrimination functions for convergent and divergent stimuli, (2) of greater discrimination for stimuli of 45 min of retinal disparity than for the stimuli of 15 min disparity, (3) of greater variability for the stimuli of greater disparity, and (4) of the use by nonanomalous subjects of at least two different processing mechanisms for stimuli of different disparity classes. The results do not support the prediction (1) of different processing mechanisms for foveal stimuli differing in figure-ground contrast or (2) of greater usefulness for monocular stimuli as a null disparity reference condition, as compared with binocular null disparity stimuli. Similar results were found for two stimulus shapes, a bar and a disk of equal area. Unreliability of subjects’ response systems was suggested as a factor in the prediction of figure-ground contrast changes and as a factor in the classification of subjects as stereo anomalous. The pattern of accuracy of discrimination between classes of disparity stimuli also raises questions of the adequacy of the simple stereopsis model.