In the natural environment, visual selection is accomplished by a system of nested effectors, moving the head and body within space and the eyes within the visual field. However, it is not yet known if the principles of selection for these different effectors are the same or different. We used a novel gaze-contingent display in which an asymmetric window of visibility (a horizontal or vertical slot) was yoked to either head or eye position. Participants showed highly systematic changes in behaviour, revealing clear differences in the principles underlying selection by eye and head. Eye movements were more likely to move in the direction of visible information—horizontally when viewing with a horizontal slot, and vertically with a vertical slot. Head movements showed the opposite and complementary pattern, moving to reveal new information (e.g. vertically with a horizontal slot and vice versa). These results are consistent with a nested system in which the head favours exploration of unknown regions, while the eye exploits what can be seen with finer-scale saccades.