Binocular vision is traditionally treated as two processes: the fusion of similar images, and the interocular suppression of dissimilar images (e.g. binocular rivalry). Recent work has demonstrated that interocular suppression is phase-insensitive, whereas binocular summation occurs only when stimuli are in phase. But how do these processes affect our perception of binocular contrast? We measured perceived contrast using a matching paradigm for a wide range of interocular phase offsets (0–180°) and matching contrasts (2–32%). Our results revealed a complex interaction between contrast and interocular phase. At low contrasts, perceived contrast reduced monotonically with increasing phase offset, by up to a factor of 1.6. At higher contrasts the pattern was non-monotonic: perceived contrast was veridical for in-phase and antiphase conditions, and monocular presentation, but increased a little at intermediate phase angles. These findings challenge a recent model in which contrast perception is phase-invariant. The results were predicted by a binocular contrast gain control model. The model involves monocular gain controls with interocular suppression from positive and negative phase channels, followed by summation across eyes and then across space. Importantly, this model—applied to conditions with vertical disparity—has only a single (zero) disparity channel and embodies both fusion and suppression processes within a single framework.