The stimulus selectivity of neurons in V1 is well known, as is the finding that their responses can be affected by visual input to areas outside of the classical receptive field. Less well understood are the ways selectivity is modified as signals propagate to visual areas beyond V1, such as V2. We recently proposed a role for V2 neurons in representing the higher order statistical dependencies found in images of naturally-occurring visual texture. V2 neurons, but not V1 neurons, respond more vigorously to "naturalistic" images that contain these dependencies than to "noise" images that lack them. Here, we examine the dependency of these effects on stimulus size. For most V2 neurons, the preference for naturalistic over noise stimuli was modest when presented in small patches, and gradually strengthened with increasing size, suggesting that the mechanisms responsible for this enhanced sensitivity operate over regions of the visual field that are larger than the classical receptive field. Indeed, we found that surround suppression was stronger for noise than for naturalistic stimuli, and that the preference for large naturalistic stimuli developed over a delayed time course consistent with lateral or feedback connections. These findings are compatible with a spatially broad facilitatory mechanism that is absent in V1, and suggest that a distinct role for the receptive field surround emerges in V2 along with sensitivity for more complex image structure.