Observers tracked binocular rivalry between a pair of small, foveally viewed gratings whose orientation differed between the 2 eyes. In Experiment 1, a textured annulus surrounding 1 eye's grating increased the total duration of exclusive visibility of the grating only when the grating-annulus separation was less than 0.5 degree. In Experiment 2, observers tracked the visibility of a monocular annulus that surrounded a foveally viewed grating that was either engaged in rivalry or fused with a grating alone viewed by the other eye. The visibility of the annulus was greater when the grating it surrounded was not undergoing rivalry fluctuations. In Experiment 3, the predominance of a rival grating was greater when the contours in the surrounding annulus were orthogonal to those of the rival grating. In Experiment 4, total exclusive visibility of a given grating-annulus target was greater when the grating and the annulus contained the same orientation.