Stereo-transparency is an intriguing, but not well-understood, phenomenon. In the present experiment, we simultaneously manipulated the number of overlaid planes, density of elements, and depth separation between the planes in random dot stereograms to evaluate the constraints on stereoscopic transparency. We used a novel task involving identification of patterned planes among the planes constituting the stimulus. Our data show that observers are capable of segregating up to six simultaneous overlaid surfaces. Increases in element density or number of planes have a detrimental effect on the transparency percept. The effect of increasing the inter-plane disparity is strongly influenced by other stimulus parameters. This latter result can explain a difference in the literature concerning the role of inter-plane disparity in perception of stereo-transparency. We argue that the effects of stimuli parameters on the transparency percept can be accounted for not only by inhibitory interactions, as has been suggested, but also by the inherent properties of disparity detectors.