When our two eyes view incongruent images, we experience binocular rivalry: An ongoing cycle of dominance periods of either image and transition periods when both are visible. Two key forces underlying this process are adaptation of and inhibition between the images' neural representations. Models based on these factors meet the constraints posed by data on dominance periods, but these are not very stringent. We extensively studied contrast dependence of dominance and transition durations and that of the occurrence of return transitions: Occasions when an eye loses and regains dominance without intervening dominance of the other eye. We found that dominance durations and the incidence of return transitions depend similarly on contrast; transition durations show a different dependence. Regarding dominance durations, we show that the widely accepted rule known as Levelt's second proposition is only valid in a limited contrast range; outside this range, the opposite of the proposition is true. Our data refute current models, based solely on adaptation and inhibition, as these cannot explain the long and reversible transitions that we find. These features indicate that noise is a crucial force in rivalry, frequently dominating the deterministic forces.