To test this hypothesis, we studied the spatiotemporal frequency tuning of MT neurons and directionally selective V1 cells in anesthetized macaques, using individual briefly presented sinusoidal gratings as stimuli. We tailored the stimulus ensemble to each cell's response characteristics and compared the Cartesian- and planar-separable models of neuronal tuning. In V1, our results depended on the cells' selectivity. For cells narrowly tuned for orientation and spatial frequency, both models make similar predictions and cannot be distinguished. When tuning was broader, however, the Cartesian-separable model consistently provided a better description of cell responses than the planar model. Most MT neurons were relatively broadly tuned in both orientation and spatial frequency, allowing the models to be distinguished. Some MT neurons were better described by the planar model than the Cartesian model. Others, however, displayed the separable spatiotemporal receptive field structure seen in V1, despite broad tuning. A few cells could not be classified. We wondered whether the cells showing planar-separable tuning might be more pattern selective than those showing Cartesian separability, but we found no such relationship. We conclude that some (but not all) MT cells' tuning is organized, as predicted, according to their velocity preferences.