Motion selectivity in primary visual cortex (V1) is approximately separable in orientation, spatial frequency, and temporal frequency ("frequency-separable"). Models for area MT neurons posit that their selectivity arises by combining direction-selective V1 afferents whose tuning is organized around a tilted plane in the frequency domain, specifying a particular direction and speed ("velocity-separable"). This construction explains "pattern direction selective" MT neurons, which are velocity-selective but relatively invariant to spatial structure, including spatial frequency, texture and shape. Surprisingly, when tested with single drifting gratings, most MT neurons' responses are fit equally well by models with either form of separability. However, responses to plaids (sums of two moving gratings) tend to be better described as velocity-separable, especially for pattern neurons. We conclude that direction selectivity in MT is primarily computed by summing V1 afferents, but pattern-invariant velocity tuning for complex stimuli may arise from local, recurrent interactions.