To find out how the representations of structured visual objects depend on the co-occurrence statistics of their constituents, we exposed subjects to a set of composite images with tight control exerted over (1) the condi- tional probabilities of the constituent fragments, and (2) the value of Bar- low’s criterion of “suspicious coincidence” (the ratio of joint probability to the product of marginals). We then compared the part verification re- sponse times for various probe/target combinations before and after the exposure. For composite probes, the speedup was much larger for tar- gets that contained pairs of fragments perfectly predictive of each other, compared to those that did not. This effect was modulated by the sig- nificance of their co-occurrence as estimated by Barlow’s criterion. For lone-fragment probes, the speedup in all conditions was generally lower than for composites. These results shed light on the brain’s strategies for unsupervised acquisition of structural information in vision.