Does the shift from binocular rivalry to fusion or stereopsis take time? We measured stereoacuity after rivalry suppression of one half-image of a stereoacuity line target. After the observer signalled that the single stereo half-image had been suppressed, the other half-image was presented for a variable duration. Stereoacuity thresholds were elevated for 150-200 ms. A control experiment demonstrated that the threshold elevation was due to rivalry suppression per se, rather than masking effects associated with the rivalry-inducing target. Monocular Vernier thresholds, measured as the smallest identifiable abrupt shift in the upper line of an aligned Vernier target that had previously been suppressed by rivalry, were elevated for a much longer duration. This result shows that an appropriately matched stereo pair can break rivalry suppression more easily than can monocular changes in position. With the aid of a similar paradigm, we also measured the duration needed to detect a disparate feature in a random-dot stereogram after rivalry suppression of one half-image of the stereogram. Observers could correctly identify the location of the disparate feature (upper or lower visual field) when the other half-image was presented for a duration ranging from 150-650 ms. In the absence of the matching half-image, the first half-image was suppressed by the rival target for a far longer duration (a few seconds). These findings show that although stereopsis and fusion terminate rivalry, both are initially disrupted for a few hundred milliseconds by rivalry suppression.