At the onset of bistable stimuli, the brain needs to choose which of the competing perceptual interpretations will first reach awareness. Stimulus manipulations and cognitive control both influence this choice process, but the underlying mechanisms and interactions remain poorly understood. Using intermittent presentation of bistable visual stimuli, we demonstrate that short interruptions cause perceptual reversals upon the next presentation, whereas longer interstimulus intervals stabilize the percept. Top-down voluntary control biases this process but does not override the timing dependencies. Extending a recently introduced low-level neural model, we demonstrate that percept-choice dynamics in bistable vision can be fully understood with interactions in early neural processing stages. Our model includes adaptive neural processing preceding a rivalry resolution stage with cross-inhibition, adaptation, and an interaction of the adaptation levels with a neural baseline. Most importantly, our findings suggest that top-down attentional control over bistable stimuli interacts with low-level mechanisms at early levels of sensory processing before perceptual conflicts are resolved and perceptual choices about bistable stimuli are made.