Humans make rapid movements of their eyes several times a second that enable them to examine objects located at different positions in space with both of their eyes. Much of our understanding of these binocular movements comes from studies using experienced observers performing repetitive, unnatural tasks. But what eye movements are made when naïve observers perform tasks demanding specific binocular visual information? We examined the binocular eye movements produced by observers performing two tasks differing in the visual information needed for their completion. Our motivation for doing this was to examine the role and function of binocular eye movements when making decisions. We considered the fixation strategies adopted by observers, the effects of the task on the dynamics of saccadic eye movements, and the combination of vergence and version in gaze shifts. We report that the task-dependent use of visual information can have a strong influence on the patterns of fixations, whilst not influencing saccade dynamics. Our data provide some support for the notion that observers choose and fixate a notional reference point in the scene when making judgments about depth structure.