Most models of visual search are based on the intuition that humans choose fixation locations containing features that best match the features of the target. The optimal version of this feature-based strategy is what we term "maximum a posteriori (MAP) search." Alternatively, humans could choose fixations that maximize information gained about the target's location. We term this information-based strategy "ideal search." Here we compare eye movements of human, MAP, and ideal searchers in tasks where known targets are embedded at unknown locations within random backgrounds having the spectral characteristics of natural scenes. We find that both human and ideal searchers preferentially fixate locations in a donut-shaped region around the center of the circular search area, with a high density of fixations at top and bottom, while MAP searchers distribute their fixations more uniformly, with low density at top and bottom. Our results argue for a sophisticated search mechanism that maximizes the information collected across fixations.