We explore the relative utility of shape from shading and binocular disparity for depth perception. Ray-traced images either featured a smooth surface illuminated from above (shading-only) or were defined by small dots (disparity-only). Observers judged which of a pair of smoothly curved convex objects had most depth. The shading cue was around half as reliable as the rich disparity information for depth discrimination. Shading- and disparity-defined cues where combined by placing dots in the stimulus image, superimposed upon the shaded surface, resulting in veridical shading and binocular disparity. Independently varying the depth delivered by each channel allowed creation of conflicting disparity-defined and shading-defined depth. We manipulated the reliability of the disparity information by adding disparity noise. As noise levels in the disparity channel were increased, perceived depths and variances shifted toward those of the now more reliable shading cue. Several different models of cue combination were applied to the data. Perceived depths and variances were well predicted by a classic maximum likelihood estimator (MLE) model of cue integration, for all but one observer. We discuss the extent to which MLE is the most parsimonious model to account for observer performance.