Upright hollow human faces produce among the strongest depth-inversion illusions (DIIs), but why? We considered the role of depth undulations by comparing four types of hollow objects: An ellipsoid, a human mask, and two symmetric ‘Martian’ masks, which wavered in depth like the human mask but which lacked face-like features. Illusion strength was quantified either as the critical viewing distance at which the 3-D percept switched between convex and concave (experiment 1) or as the proportion of time (‘predominance’) that observers experienced DII from a fixed intermediate viewing distance (experiment 2). Critical distances were smallest—and hence the illusion was strongest—for the upright human mask; the remaining objects produced undifferentiated critical distance values. The predominance results were more fine-grained: illusions were experienced most often for the upright human mask, least often for the hollow ellipsoid, and to an intermediate extent for the Martian and upside-down human masks. These results suggest: (1) an upside-down human mask and a surface with nonface features undulating in depth are equivalent for the purposes of generating DIIs; (2) depth undulations contribute to DII; and (3) such undulations are most effective when structured into an upright human face.