The nature of competition underlying perceptual alternations in binocular rivalry remains controversial. Interocular swapping of rivalrous stimuli can result in either slow irregular perceptual alternations that bridge multiple interocular switches or fast regular alternations that are time locked to the stimulus exchanges. We labeled either the inputs to the eyes or the individual rivalrous stimuli using temporal frequency and contrast tagging. Tagging of eye-of-origin signals enhanced the fast regular perceptual alternations associated with eye rivalry, while stimulus tagging shifted perception towards slow irregular alternations characteristic of stimulus rivalry. Thus, the type of competition in binocular rivalry can be biased based on additional cues in the visual inputs. The results are consistent with a model in which the brain combines information across multiple visual features to resolve ambiguities in visual inputs.