Recent studies of redundancy gain indicate that it is especially large when redundant stimuli are presented to different hemispheres of an individual without a functioning corpus callosum. This suggests the hypothesis that responses to redundant stimuli are speeded partly because both hemispheres are involved in the activation of the response. A simple formal model incorporating this idea is developed and then elaborated to account for additional related findings. Predictions of the latter model are in good qualitative agreement with data from a number of sources, and there is neuroanatomic and psychophysiological support for its underlying structure.