A behavioural advantage is found across a wide range of stimuli when two targets are presented in opposite hemifields compared with those targets being presented together in one hemifield, or one target being presented alone. This advantage for responses to multiple targets versus a single target is often termed redundancy gain. Here we report on the findings of two experiments investigating redundancy gain in binocular rivalry. Experiment 1 presented a rival pair in one hemifield with an additional image presented to both eyes in the opposite hemifield. There was a weak effect of this stable image on the perceived dominance of the images within the rival pair. Experiment 2 presented a second rival pair in either the same or opposite hemifield and showed that instances of joint predominance were greater when the two pairs were presented in opposite hemifields than within the same hemifield. Therefore, the findings suggest that redundancy gain may be extended to stimuli presented under binocular rivalry conditions.