An influential theory of the function of early processing in the visual cortex is that it forms an efficient coding of ecologically valid stimuli. In particular, correlations and differences between visual signals from the two eyes are believed to be of great importance in solving both depth from disparity and binocular fusion. Techniques such as independent-component analysis have been developed to learn efficient codings from natural images; these codings have been found to resemble receptive fields of simple cells in V1. However, the extent to which this approach provides an explanation of the functionality of the visual cortex is still an open question. We compared binocular independent components with physiological measurements and found a broad range of similarities along with a number of key differences. In common with physiological measurements, we found components with a broad range of both phase- and position-disparity tuning. However, we also found a larger population of binocularly anticorrelated components than have been found physiologically. We found components focused narrowly on detecting disparities proportional to half-integer multiples of wavelength rather than the range of disparities found physiologically. We present the results as a detailed analysis of phase and position disparities in Gabor-like components generated by independent-component analysis trained on binocular natural images and compare these results to physiology. We find strong similarities between components learned from natural images, indicating that ecologically valid stimuli are important in understanding cortical function, but with significant differences that suggest that our current models are incomplete.