During binocular rivalry visual consciousness fluctuates between two dissimilar monocular images. We investigated the role of attention in this phenomenon by comparing event-related potentials (ERPs) when binocular-rivalry stimuli were attended with when they were unattended. Stimuli were dichoptic, orthogonal gratings that yielded binocular rivalry and dioptic, identically oriented gratings that yielded binocular fusion. Events were all possible orthogonal changes in orientation of one or both gratings. We had two attention conditions: In the attend-to-grating condition, participants had to report changes in perceived orientation, focussing their attention on the gratings. In the attend-to-fixation condition participants had to report changes in a central fixation target, taking attention away from the gratings. We found, surprisingly, that attending to rival gratings yielded a smaller ERP component (the N1, from 160-210 ms) than attending to the fixation target. To explain this paradoxical effect of attention, we propose that rivalry occurs in the attend-to-fixation condition (we found an ERP signature of rivalry in the form of a sustained negativity from 210-300 ms) but that the mechanism processing the stimulus changes is more adapted in the attend-to-grating condition than in the attend-to-fixation condition. This is consistent with the theory that adaptation gives rise to changes of visual consciousness during binocular rivalry.