In five experiments, we investigated the detection of symmetry (i.e., translation plus reflection) or repetition (i.e., translation alone) between two vertical jagged contours. The complexity of the two contours was manipulated, as was their figure-ground assignment; the two contours either belonged to a common object "inside" them, to two separate objects "outside" them, or to two separate objects each to the right of one contour. Replicating Baylis and Driver (1994), symmetry judgements were unaffected by contour complexity when made within a single shape, implying a parallel process operating efficiently across contour discontinuities. However, all the other conditions yielded substantially slower judgements as complexity increased, suggesting either effortful point-by-point comparisons, or a highly inefficient parallel process. In agreement with Baylis and Driver (1995a), symmetry perception was harder when figure-ground assignment turned convexities along one contour into concavities along the other contour; and likewise for repetition detection. However, even when convex parts matched between the two contours, judgements were still affected by complexity unless they belonged to a common object. This supports Baylis and Driver's (1993) proposal that effortless comparisons for the layout of multiple convex parts can only be made within single perceptual objects.