The pattern of illumination on an undulating surface can be used to infer its 3-D form (shape-from-shading). But the recovery of shape would be invalid if the luminance changes actually arose from changes in reflectance. So how does vision distinguish variation in illumination from variation in reflectance to avoid illusory depth? When a corrugated surface is painted with an albedo texture, the variation in local mean luminance (LM) due to shading is accompanied by a similar modulation in local luminance amplitude (AM). This is not so for reflectance variation, nor for roughly textured surfaces. We used depth mapping and paired comparison methods to show that modulations of local luminance amplitude play a role in the interpretation of shape-from-shading. The shape-from-shading percept was enhanced when LM and AM co-varied (in-phase) and was disrupted when they were out of phase or (to a lesser degree) when AM was absent. The perceptual differences between cue types (in-phase vs out-of-phase) were enhanced when the two cues were present at different orientations within a single image. Our results suggest that when LM and AM co-vary (in-phase) this indicates that the source of variation is illumination (caused by undulations of the surface), rather than surface reflectance. Hence, the congruence of LM and AM is a cue that supports a shape-from-shading interpretation.