Binocular rivalry, the perceptual alternation between incompatible monocular stimuli, is conventionally measured by asking the subject which percept is currently visible. This is problematic because the response is unverifiable, open to response bias, and falsely assumes that the perceptual experience is binary. We overcame these limitations in a new approach that does not require subjective reporting of perceptual state. A brief test stimulus was added to one eye's inducing stimulus at random times and contrasts. The test was presented at one of two spatial locations, the subject indicated which alternative had been shown, and the correctness of the response was recorded as a function of test contrast. Given the random timing of the test stimulus, it was sometimes delivered when the tested eye was dominant and, at other times, suppressed. Accordingly, the psychometric function recorded during rivalry should be a mixture of the dominance and suppression forms of the function. This was indeed the case: The probability of a correct response during rivalry was significantly less than that obtained with a binocularly congruent stimulus. The psychometric function during rivalry was well modeled as a weighted sum of the congruence curve with an assumed suppression curve. Optimal fitting provided estimates of both suppression depth and percept predominance that corresponded closely with estimates obtained with the conventional method. We have therefore characterized rivalry without the uncertainties introduced by the subject's perceptual report. This provides a model that may be applicable to the broader field of perceptual ambiguity.