During binocular rivalry, observers sometimes perceive one complete visual object even though component features of that perceptually dominant object are distributed between the two eyes and are in rivalry against other, dissimilar features. This interocular grouping cannot be explained by models of rivalry in which one eye or the other is completely dominant at any given moment. But perhaps global interocular grouping is achieved by simultaneous local eye dominance, wherein portions of one eye's view and complementary portions of the other eye's view become dominant simultaneously. To test this possibility, we performed two experiments using relatively large, complex figures as rival targets. In one experiment we used an "eye-swap" technique to confirm that within given, local spatial regions of rivalry it was the region of an eye--not a given stimulus feature--that was usually dominant. In a second experiment, we measured dominance durations for multiple, local zones of rivalry and then created 1-min animations of a global "montage" in which dominance within local regions was governed by the distributions of dominance measured empirically. These animations included significant periods of time during which global interocular grouping was evident; observers viewed these animations intermixed with actual rivalry displays, and the resulting tracking data confirmed the similarity in global dominance of the two display types. Thus interocular grouping during rivalry does not rule out local, eye-based rivalry, although synergistic and top-down influences almost certainly provide additional force in the promotion of interocular grouping.