How do we decide where to look next? During natural, active vision, we move our eyes to gather task-relevant information from the visual scene. Information theory provides an elegant framework for investigating how visual stimulus information combines with prior knowledge and task goals to plan an eye movement. We measured eye movements as observers performed a shape-learning and -matching task, for which the task-relevant information was tightly controlled. Using computational models, we probe the underlying strategies used by observers when planning their next eye movement. One strategy is to move the eyes to locations that maximize the total information gained about the shape, which is equivalent to reducing global uncertainty. Observers' behavior may appear highly similar to this strategy, but a rigorous analysis of sequential fixation placement reveals that observers may instead be using a local rule: fixate only the most informative locations, that is, reduce local uncertainty.