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This article investigates the cognitive strategies that people use to search computer displays. Several different visual layouts are examined: unlabeled layouts that contain multiple groups of items but no group headings, labeled layouts in which items are grouped and each group has a useful heading, and a target-only layout that contains just one item. A number of plausible strategies were proposed for each layout. Each strategy was programmed into the EPIC cognitive architecture, producing models that simulate the human visual-perceptual, oculomotor, and cognitive processing required for the task. The models generate search time predictions. For unlabeled layouts, the mean layout search times are predicted by a purely random search strategy, and the more detailed positional search times are predicted by a noisy systematic strategy. The labeled layout search times are predicted by a hierarchical strategy in which first the group labels are systematically searched, and then the contents of the target group. The target-only layout search times are predicted by a strategy in which the eyes move directly to the sudden appearance of the target. The models demonstrate that human visual search performance can be explained largely in terms of the cognitive strategy that is used to coordinate the relevant perceptual and motor processes, a clear and useful visual hierarchy triggers a fundamentally different visual search strategy and effectively gives the user greater control over the visual navigation, and cognitive strategies will be an important component of a predictive visual search tool. The models provide insights pertaining to the visual-perceptual and oculomotor processes involved in visual search and contribute to the science base needed for predictive interface analysis.