How efficiently do people integrate the disconnected image fragments that fall on their eyes when they view partly occluded objects? In the present study, I used a psychophysical summation-at-threshold technique to address this question by measuring discrimination performance with both isolated and combined features of physically fragmented but perceptually complete objects. If visual completion promotes superior integration efficiency, performance with a visually completed object should exceed what would be expected from performance with the individual object parts shown in isolation. Contrary to this prediction, results showed that discrimination performance with both static and moving versions of physically fragmented but perceptually complete objects was significantly worse than would be expected from performance with their constituent parts. These results present a challenge for future theories of visual completion.