Does human vision show the contrast invariance expected of an ideal stereoscopic system for computing depth from disparity? We used random-dot stereograms to investigate the luminance contrast effect on perceived depth from disparity. The perceived depth of disparity corrugations was measured by adjusting the length of a horizontal line to match the perceived depth of the corrugations at various luminance contrasts. At each contrast, the perceived depth increased with disparity up to a critical value, decreasing with further increases in disparity. Both the maximum perceived depth and the disparity modulation level where this maximum occurred changed as a sigmoid function of luminance contrast. These results show that perceived depth from disparity depends in a complex manner on the luminance contrast in the image, providing significant limitations on depth perception at low contrasts in a lawful manner but that are incompatible with existing models of cortical disparity processing.