The human fovea and visual pathways are precisely split: information in one hemifield is initially projected to the contralateral visual cortex. This fundamental anatomical constraint on word recognition in reading has been largely ignored in eye movement research. We explore the consequences of this constraint through analyses of a large corpus of eye movement data, and demonstrate that aspects of saccade planning (target selection, initial landing position) are sensitive to both hemispheres, estimated uncertainty about the identity of the currently fixated word. We interpret these findings in terms of a hemispheric division of labour. We suggest that anatomical, visual and lexical factors all contribute to the decision of where to send the eyes next in reading.