A longstanding debate in binocular rivalry literature is whether the perceptual competition in rivalry occurs at an early or late stage of visual processing. Central to this debate is the determination of the source of the competition. Overwhelming evidence exists that local interocular differences can lead to binocular rivalry, but it is not yet clear whether interocular conflicts at the global level are sufficient to generate binocular rivalry. The current study adopted a novel stimulus that enabled the introduction of dramatic global differences between the two eyes with compatible local elements. Results show that global differences between the two eyes' images do not result in rivalry if local elements are compatible. The implication of these findings is that the registration of competing interocular information, necessary to generate binocular rivalry, is performed at an early stage of visual processing prior to global analysis of the image.