The properties of human stereoscopic mechanisms may be derived from dichoptic interaction and masking effects on stereoscopic detection thresholds in any relevant stimulus domain (spatial frequency, temporal frequency, disparity, orientation, etc.). The present study focuses on the spatial properties of mechanisms underlying stereoscopic depth detection. The computational approach is based on the full exploration of plausible model structures to characterize their idiosyncrasies, which often allows exclusion of proposed mechanisms by comparison with data obtained under conditions in which the idiosyncrasies should be expressed. For example, we conducted a detailed analysis of threshold elevation functions (TEFs) under plausible channel shapes, combination rules and masking behavior derived from previous studies. The analysis reveals that TEFs may be much narrower than and differ in shape from the underlying mechanisms. For example, only two discrete channels are required to produce TEFs peaking close to each fixed test frequency, with no relation to channel peaks. We apply this analysis to the stereospatial masking functions collected by Yang and Blake (1991) to determine the likely channel structure underlying the empirical masking performance. The analysis generally supports the two-mechanism model that they propose but shows that the assumptions underlying their estimates of the unmasked sensitivity function are incorrect. The analysis excludes stereospatial channels tuned below 2.5 c/deg, a region in which Schor, Wood, and Ogawa (1984) obtained evidence for many narrowly tuned channels by measuring disparity thresholds for targets with different peak tunings in the two eyes. Our computational model for the latter data is consistent with the lowest tuned channel being at 2.5 c/deg, this channel being narrowly tuned to dichoptic contrast differences, as described by Legge and Gu (1989) and Halpern and Blake (1988). Thus, all such stereo tuning data can be explained in a model in which all stereoscopic channels are tuned above 2.5 c/deg.