Neighboring retinal ganglion cells often spike synchronously, but the possible function and mechanism of this synchrony is unclear. Recently, the strength of the fast correlation between ON-OFF directionally selective cells of the rabbit retina was shown to be stimulus dependent. Here, we extend that study, investigating stimulus-dependent correlation among multiple ganglion-cell classes, using multi-electrode recordings. Our results generalized those for directionally selective cells. All cell pairs exhibiting significant spike synchrony did it for an extended edge but rarely for full-field stimuli. The strength of this synchrony did not depend on the amplitude of the response and correlations could be present even when the cells' receptive fields did not overlap. In addition, correlations tended to be orientation selective in a manner predictable by the relative positions of the receptive fields. Finally, extended edges and full-field stimuli produced significantly greater and smaller correlations than predicted by chance respectively. We propose an amacrine-network model for the enhancement and depression of correlation. Such an apparently purposeful control of correlation adds evidence for retinal synchrony playing a functional role in vision.