Objects in complex images appear almost constant. This is true with changes of the overall level of illumination, and somewhat true with changes of the surround around a test area. The small departures from perfect constancy, however, provide important evidence on the underlying mechanisms of constancy. First, this paper measures the departures from constancy with changes in overall luminance. Second, it measures the effects of contrast using white, gray, and black surrounds. Third, it compares the results from flat-2D transparent displays with those using 3D shapes. With 3-D paper targets, illuminated in direct light and shadow, we find the same small decrease in matching value with large decreases in illumination level (low-slope behavior) found in flat-2D transparent displays. Within the direct light and in the shade parts of the targets, the matches showed the same high-slope contrast behavior. Here, the arrangement of reflectances, illumination and depth did not affect the appearance matches made by observers. In both flat-2D transparent and complex 3-D data, observers' matches fit the simple two-step physical description. The local maxima are dependent on luminance, and other, darker areas, are dependent on spatial contrast.