When our two eyes view incompatible images, the brain invokes suppressive processes to inhibit one image, and favor the other. Two phenomena are typically observed: dichoptic masking (reduced sensitivity to one image) for brief presentations, and binocular rivalry (alternation between the two images), over longer exposures. However, it is not clear if these two phenomena arise from a common suppressive process. We investigated this by measuring both threshold elevation in simultaneous dichoptic masking and mean percept durations in rivalry, whilst varying relative stimulus orientation. Masking and rivalry showed significant correlations, such that strong masking was associated with long dominance durations. A second experiment suggested that individual differences across both measures are also correlated. These findings are consistent with varying the magnitude of interocular suppression in computational models of both rivalry and masking, and imply the existence of a common suppressive process. Since dichoptic masking has been localised to the monocular neurons of V1, this is a plausible first stage of binocular rivalry.