When incompatible images are presented to corresponding regions of each eye, perception alternates between the two monocular views (binocular rivalry). In this study, we have investigated how involuntary (exogenous) and voluntary (endogenous) attention can influence the perceptual dominance of one rival image or the other during contour rivalry. Subjects viewed two orthogonal grating stimuli that were presented to both eyes. Involuntary attention was directed to one of the grating stimuli with a brief change in orientation. After a short period, the cued grating was removed from the image in one eye and the uncued grating was removed from the image in the other eye, generating binocular rivalry. Subjects usually reported dominance of the cued grating during the rivalry period. We found that the influence of the cue declined with the interval between its onset and the onset of binocular rivalry in a manner consistent with the effect of involuntary attention. Finally, we demonstrated that voluntary attention to a grating stimulus could also influence the ongoing changes in perceptual dominance that accompany longer periods of binocular rivalry Voluntary attention did not increase the mean dominance period of the attended grating, but rather decreased the mean dominance period of the non-attended grating. This pattern is analogous to increasing the perceived contrast of the attended grating. These results suggest that the competition during binocular rivalry might be an example of a more general attentional mechanism within the visual system.