Many researchers have proposed that, for the purpose of recognition, human vision parses shapes into component parts. Precisely how is not yet known. The minima rule for silhouettes (Hoffman & Richards, 1984) defines boundary points at which to parse but does not tell how to use these points to cut silhouettes and, therefore, does not tell what the parts are. In this paper, we propose the short-cut rule, which states that, other things being equal, human vision prefers to use the shortest possible cuts to parse silhouettes. We motivate this rule, and the well-known Petter's rule for modal completion, by the principle of transversality. We present five psychophysical experiments that test the short-cut rule, show that it successfully predicts part cuts that connect boundary points given by the minima rule, and show that it can also create new boundary points.