We investigated the ability of human observers to discriminate an important global 3-D structural property, namely volume, of motion-defined objects. We used convex transparent wire-frame objects consisting of about 12 planar triangular facets. Two objects, vertically separated by 7°, were shown simultaneously on a computer display. Both revolved at 67°/sec around a common vertical axis through their centers of mass. Observers watched the objects monocularly for an average of three full rotations before they responded. We measured volume discrimination as a function of absolute volume (3-48 cm3; 1 m viewing distance) and shape (cubes, rods, and slabs of different regularity). We found that (1) volume discrimination performance can be described by Weber's law, (2) Weber fractions depend strongly on the particular combination of shapes used (regular shapes, especially cubes, are easiest to compare, and similar shapes are easier to compare than different shapes), and (3) humans use a representation of volume that is more veridical and stable in the sense of repeatability than a strategy based on the average visible (2-D) area would yield.