Although Attneave (1954, Psychological Review 61 183 – 193) and Biederman (1987, Psychological Review 94 115 – 147) have argued that curved contour segments are most important in shape perception, Kennedy and Domander (1985, Perception 14 367 – 370) showed that fragmented object contours are more identifiable when straight segments are shown. Based on the set of line drawings published by Snodgrass and Vanderwart (1980, Journal of Experimental Psychology: Human Learning and Memory 6 174 – 215), we have made outline versions that can be used to investigate this issue with a larger and more heterogeneous stimulus set. Fragments were placed either around the “salient” points or around the midpoints (points midway between two salient points), creating curved versus relatively straight fragments when the original outline was fragmented (experiment 1), or angular and straight fragments when straight-line versions were fragmented (experiment 2). We manipulated fragment length in every experiment except the last one, in which we presented only selected points (experiment 3). While fragmented versions were on average more identifiable when straight fragments are shown, certain objects were more identifiable when the curved segments or the angles were shown. A tentative explanation of these results is presented in terms of an advantage for straight segments during grouping processes for outlines with high part salience, and an advantage for curved segments during matching processes for outlines with low part salience.