Natural scenes are known to have a variety of similar statistical properties. In particular, scenes are found to have Fourier power spectra that fall off with frequency as 1/frequency^2 (amplitude falls as 1/f). One popular theory of retinal ganglion cell processing suggests that the goal of this unit is to provide a decorrelated or "whitened" output given natural stimuli. That is, by virtue of their center-surround receptive field organization, ganglion cells exploit the predictable statistics in scenes in order to represent the input more efficiently. But there are a number of spatial decorrelation strategies that do not require a receptive field organization like that found in primate retinal ganglion cells. In this study, we compare different decorrelation strategies for natural scene stimuli to determine the relative advantages of center-surround organization. We show that the localized center-surround organization produces more than decorrelation: it also gives a more sparse response. In addition, we argue that the relative sensitivity of ganglion cells as a function of size--for at least P-type ganglion cells--supports the notion that these cells achieve some degree of response equalization when given natural scenes. We also consider the possible role played by the neurons' known nonlinearities in producing a more efficient response.