A common approach to the problem of contour interpolation is based on the calculus of variations. The optimal interpolating contour is taken to be one that minimizes a given smoothness functional. Two important such functionals are total curvature (or bending energy) and variation in curvature. We analyzed contours extrapolated by human observers given arcs of Euler spirals that disappeared behind an occluding surface. Irrespective of whether the Euler spirals had increasing or decreasing curvature as they approached the occluding edge, visually-extrapolated contours were found to be characterized by decaying curvature. This curvature decay is modeled in terms of a Bayesian interaction between probabilistically-expressed constraints to minimize curvature and minimize variation in curvature. The analysis suggests that using fixed smoothness functionals is not appropriate for modeling human vision. Rather, the relative weights assigned to different probabilistic shape constraints may vary as a function of distance from the point(s) of occlusion. Implications are discussed for computational models of shape completion.