Experiments were performed to assess the response of the human visual system to dynamic random-dot patterns composed of disparity mixtures. In Experiment 1, the perceived depth and relative stability of two patterns were compared; one pattern depicted two transparent layers of dots, and the other depicted a volume of dots. Two effects were found: (1) the volume pattern exhibited a large degree of disparity averaging; and (2) asymmetries were observed in the relative stability of these two patterns. Experiment 2 was designed to determine whether these findings could be attributed to spatially localized processes occurring at the location of disparity discontinuities. This was accomplished by introducing unpaired noise points localized either along the disparity discontinuities or in the center of the layered and volume patterns. The amount of depth averaging and the direction of the asymmetry did not appear to depend on processes localized along the disparity discontinuities. Results of these experiments, taken in conjunction with those of previous studies, suggest that hysteresis is independent of cooperative persistence mechanisms.