Disparity-based depth is not perceived in densely textured, anticorrelated random-dot stereograms (RDSs) whose elements carry opposite signs of brightness contrast on corresponding loci, as extant data show. We observed global depth in anticorrelated RDSs flashed repetitively with an interocular delay. During the delay time, a dot array in one eye was paired with a gray frame in the other eye and thus could interact with the negative afterimage of the contralateral dot array. A correlated RDS (e.g. 8 min arc dots, 50% density, 15-msec flash duration) lost depth with delays > 45 msec. An anticorrelated RDS, that was otherwise identical, showed robust depth when flashed with an interocular delay of some 60 msec. A delay was not always necessary to produce depth. At low dot density (1-2%), anticorrelated RDSs showed disparity-dependent local depth even when displayed continuously, or flashed simultaneously; as dot density alone was increased, depth was progressively lost. To make global depth visible in a dense RDS flashed with an interocular delay, the internal response had to be strongly biphasic. Our results support the generally held notion that cyclopean depth signals emerge exclusively from same-sign binocular cortical filters. However, the exclusionary rule may be invalid with respect to the processing of coarse local depth with figural stimuli. Relative depth between a pair of small dots was easily perceived when one of the dots was in opposite contrast, but the depth threshold was then about 0.5 log unit higher than with the same-contrast pair of dots indicating that the internal effects of contrast have not all lost their sign prior to binocular disparity processing. It remains to be determined whether depth can be perceived from edges of opposite contrast.