It has recently been shown that an increase of the relief height of a glossy surface positively correlates with the perceived level of gloss (Y.-H. Ho, M. S. Landy, & L. T. Maloney, 2008). In the study presented here we investigated whether this relation could be explained by the finding that glossiness perception correlates with the skewness of the luminance histogram (I. Motoyoshi, S. Nishida, L. Sharan, & E. H. Adelson, 2007). First, we formally derived a general relation between the depth range of a Lambertian surface, the illumination direction and the associated image intensity transformation. From this intensity transformation we could numerically simulate the relation between relief stretch and the skewness statistic. This relation predicts that skewness increases with increasing surface depth. Furthermore, it predicts that the correlation between skewness and illumination can be either positive or negative, depending on the depth range. We experimentally tested whether changes in the depth range and illumination direction alter the appearance. We indeed find a convincingly strong illusory gloss effect on stretched Lambertian surfaces. However, the results could not be fully explained by the skewness hypothesis. We reinterpreted our results in the context of the bas-relief ambiguity (P. N. Belhumeur, D. J. Kriegman, & L. Yuille, 1999) and show that this model qualitatively predicts illusory highlights on locations that differ from actual specular highlight locations with increasing illumination direction.