Selective attention in multidimensional displays has usually been examined using search tasks requiring the detection of a single target. We examined the ability to perceive a spatial structure in multi-item subsets of a display that were defined either conjunctively or disjunctively. Observers saw two adjacent displays and indicated whether the to-be-selected items within the two displays matched in terms of their spatial structure (the identity of the corresponding items within these subsets was not relevant to the task). The observers in our study could readily perceive conjunctively defined subsets, but had great difficulty with disjunctively defined subsets. The results pose a challenge to the popular idea that attention is guided by a "priority map" that sums bottom-up and top-down factors, whereas they are directly predicted by Boolean map theory of visual attention. (Contains 4 figures, 1 table, and 1 footnote.)