Human stereo vision can resolve remarkably small depth differences between two stimuli, but the smallest resolvable difference is usually that between stimuli located near the plane of fixation. As distance from this plane increases, so does the smallest detectable increment in disparity. We examined this loss of resolution by comparing disparity discrimination thresholds for single-scale and multi-scale stimuli as a function of the pedestal disparity. For single-scale gratings, disparity thresholds display phase constancy; thus, their spatial thresholds vary reciprocally with grating spatial frequency. For multi-scale gratings, with components separated in frequency by two or three octaves, disparity thresholds display two types of interaction between coarse-scale and fine-scale components: facilitation when pedestal disparities are moderate and interference when they are large. The facilitation extends the disparity range that yields the low thresholds associated with fine-scale components, limiting the loss of disparity resolution for multi-scale stimuli.