Symmetry is usually easier to detect within a single object than in two objects (one-object advantage), while the reverse is true for repetition (two-objects advantage). This interaction between regularity and number of objects could reflect an intrinsic property of encoding spatial relations within and across objects or it could reflect a matching strategy. To test this, regularities between two contours (belonging to a single object or two objects) had to be detected in two experiments. Projected three-dimensional (3-D) objects rotated in depth were used to disambiguate figure-ground segmentation and to make matching based on simple translations of the two-dimensional (2-D) contours unlikely. Experiment 1 showed the expected interaction between regularity and number of objects. Experiment 2 used two-objects displays only and prevented a matching strategy by also switching the positions of the two objects. Nevertheless, symmetry was never detected more easily than repetition in these two-objects displays. We conclude that structural coding, not matching strategies, underlies the one-object advantage for symmetry and the two-objects advantage for repetition.