We report two experiments assessing how observers interpolate partly-occluded contours induced by pairs of line segments that disappeared behind an occluder. On each trial observers iteratively adjusted the location and orientation of a short line probe that could be moved vertically within the region of occlusion. They were instructed to set the line probe to be tangent to the occluded contour. The line probe could appear at one of six horizontal offsets and the inducer pairs on some trials were relatable (the inducers could be joined by a smooth curve without a point of inflection) and on other trials non-relatable. We interpreted the settings as estimates of the location and gradient (slope) of the contour in the region of occlusion. We tested whether the resulting visual estimates of location and gradient were consistent with any single smooth contour. When inducers were relatable, estimates of location and gradient were mutually consistent for all observers and could be modeled as polynomials of 5 th or lower degree. When the inducers were non-relatable, the consistency of location and gradient settings deteriorated, indicating that there can be no single smooth curve that accounts for observers' judgments. We discuss the implication of these results for models of human visual interpolation.