In binocular rivalry, the conscious percept alternates stochastically between two images shown to the two eyes. Both suppressed and dominant images form afterimages (AIs) whose strength depends on the perceptual state during induction. Counterintuitively, when these two AIs rival, the AI of the previously suppressed percept gains initial dominance, even when it is weaker. Here, we examined rivalry between afterimages, between real images, and between both to examine eye-based and binocular contributions to this effect. In all experiments, we found that for both AIs and real images, the suppressed percept consistently gained initial dominance following a long suppression period. Dominance reversals failed to occur following short suppression periods and depended on an abrupt change (removal) of the stimulus. With real images, results were replicated also when eye channels were exchanged during the abrupt change. The initial dominance of the weaker, previously suppressed percept is thus not due to its weaker contrast, to it being an afterimage, or to monocular adaptation effects as previously suggested. Instead, it is due to binocular, higher level effects that favor a perceptual switch after prolonged dominance. We discuss a plausible neural account for these findings in terms of neural interactions between binocular and eye-related stages.