Certain pairs of visual patterns, when superimposed as if transparent, elicit a wavering percept in which one or the other pattern can enjoy temporary periods of exclusive visibility. This multistable perceptual phenomenon is called monocular rivalry or pattern rivalry (PR) and is most pronounced when the component patterns are faint and devoid of detail. The principal mechanisms that give rise to PR continue to be a topic of speculation. In the present study, we examine the determinants of exclusive dominance during PR using a novel stimulus in which a central portion is free of conflict. By observing the properties of suppression in this so-called rivalry-free region, we demonstrate that perception is driven largely by the global and holistic interpretation of the patterns, rather than by the need to resolve local spatial conflict. The suppression of this central region was often complete and varied as a function of the parameters of the global stimulus, including the size of the surround region, its ocular configuration, and stereoscopic depth ordering. Suppression also varied as a function of pattern continuity across the central region as well as with the temporal offset of the overlapping components. These findings demonstrate that the visibility or invisibility of a pattern is not fundamentally a product of local processing, but is instead shaped by the brain's global interpretive assumptions regarding the composition of the stimulus.