During binocular rivalry (BR), conflicting monocular images are alternately suppressed from awareness. During suppression of an image, contrast sensitivity for probes is reduced by approximately 0.3-0.5 log units relative to when the image is in perceptual dominance. Previous studies on rivalry suppression have led to controversies concerning the nature and extent of suppression during BR. We tested for feature-specific suppression using orthogonal rivaling gratings and measuring contrast sensitivity to small grating probes at a range of orientations in a 2AFC orientation discrimination task. Results indicate that suppression is not uniform across orientations: suppression was much greater for orientations close to that of the suppressed grating. The higher suppression was specific to a narrow range around the suppressed rival grating, with a tuning similar to V1 orientation bandwidths. A similar experiment tested for spatial frequency tuning and found that suppression was stronger for frequencies close to that of the suppressed grating. Interestingly, no tuned suppression was observed when a flicker-and-swap paradigm was used, suggesting that tuned suppression occurs only for lower-level, interocular rivalry. Together, the results suggest there are two components to rivalry suppression: a general feature-invariant component and an additional component specifically tuned to the rivaling features.