There has been a growing interest in understanding the computations involved in the processes underlying visual segmentation and interpolation in conditions of occlusion. P. J. Kellman, P. Garrigan, T. F. Shipley, and B. P. Keane and M. K. Albert defended the view that identical contour interpolation mechanisms underlie modal and amodal completion. In the current rejoinder, the author provides further psychophysical evidence against this view and argues that no physiological data support the claim that modal and amodal contours are represented identically at any stage of processing. The author also shows that the illusory glass surfaces that Kellman et al. and Albert upheld as evidence against his arguments about luminance constraints in completion are explained by theoretical principles that he has previously articulated, and variants of these illusions receive no explanation within either of the models Kellman et al. and Albert propose. The author shows that the principles needed to explain these percepts embody fundamental asymmetries in the way that relative depth shapes segmentation and interpolation processes and that models of completion that lack these constraints--such as P. J. Kellman, P. Garrigan, and T. F. Shipley's and M. K. Albert's--cannot account for a host of documented completion phenomena.