Human stereopsis can operate in dense “cyclopean” images containing no monocular objects. This is believed to depend on the computation of binocular correlation by neurons in primary visual cortex (V1). The observation that humans perceive depth in half-matched random-dot stereograms, although these stimuli have no net correlation, has led to the proposition that human depth perception in these stimuli depends on a distinct “matching” computation possibly performed in extrastriate cortex. However, recording from disparity-selective neurons in V1 of fixating monkeys, we found that they are in fact able to signal disparity in half-matched stimuli. We present a simple model that explains these results. This reinstates the view that disparity-selective neurons in V1 provide the initial substrate for perception in dense cyclopean stimuli, and strongly suggests that separate correlation and matching computations are not necessary to explain existing data on mixed correlation stereograms.