Most existing computational models of the visual perception of three-dimensional shape from texture are based on assumed constraints about how texture is distributed on visible surfaces. The research described in the present article was designed to investigate how violations of these assumptions influence human perception. Observers were presented with images of smoothly curved surfaces depicted with different types of texture, whose distribution of surface markings could be both anisotropic and inhomogeneous. Observers judged the pattern of ordinal depth on each object by marking local maxima and minima along designated scan lines. They also judged the apparent magnitudes of relative depth between designated probe points on the surface. The results revealed a high degree of accuracy and reliability in all conditions, except for a systematic underestimation of the overall magnitude of surface relief. These findings suggest that human perception of three-dimensional shape from texture is much more robust than would be reasonable to expect based on current computational models of this phenomenon.