When two qualitatively different stimuli are presented at the same time, one to each eye, the stimuli can either integrate or compete with each other. When they compete, one of the two stimuli is alternately suppressed, a phenomenon called binocular rivalry [1,2]. When they integrate, observers see some form of the combined stimuli. Many different properties (for example, shape or color) of the two stimuli can induce binocular rivalry. Not all differences result in rivalry, however. Visual 'beats', for example, are the result of integration of high-frequency flicker between the two eyes [3,4], and are thus a binocular fusion phenomenon. It remains in dispute whether binocular fusion and rivalry can co-exist with one another [5-7]. Here, we report that rivalry and beats, two apparently opposing phenomena, can be perceived at the same time within the same spatial location. We hypothesized that the interocular difference in visual attributes that are predominantly processed in the Parvocellular pathway will lead to rivalry, and differences in visual attributes that are predominantly processed in the Magnocellular pathway tend to integrate. Further predictions based on this hypothesis were tested and confirmed.