Binocular rivalry is the alternating percept that can result when the two eyes see different scenes. Recent psychophysical evidence supports the notion that some aspects of binocular rivalry bear functional similarities to other bistable percepts. We build a model based on the hypothesis (Logothetis & Schall, 1989; Leopold & Logothetis, 1996; Logothetis, Leopold & Sheinberg, 1996) that alternation can be generated by competition between top-down cortical explanations for the inputs, rather than by direct competition between the inputs. Recent neurophysiological evidence shows that some binocular neurons are modulated with the changing percept; others are not, even if they are selective between the stimuli presented to the eyes. We extend our model to a hierarchy to address these effects.