Perceptual bistability occurs when a physical stimulus gives rise to two distinct interpretations that alternate irregularly. Noise and adaptation processes are two possible mechanisms for switching in neuronal competition models that describe the alternating behaviors. Either of these processes, if strong enough, could alone cause the alternations in dominance. We examined their relative role in producing alternations by studying models where by smoothly varying the parameters, one can change the rhythmogenesis mechanism from being adaptation-driven to noise-driven. In consideration of the experimental constraints on the statistics of the alternations (mean and shape of the dominance duration distribution and correlations between successive durations) we ask whether we can rule out one of the mechanisms. We conclude that in order to comply with the observed mean of the dominance durations and their coefficient of variation, the models must operate within a balance between the noise and adaptation strength-both mechanisms are involved in producing alternations, in such a way that the system operates near the boundary between being adaptation-driven and noise-driven.