Directionally selective (DS) neurons are found in the retina and lateral geniculate nucleus (LGN) of rabbits and rodents, and in rabbits, LGN DS cells project to primary visual cortex. Here, we compare visual response properties of LGN DS neurons with those of layer 4 simple cells, most of which show strong direction/orientation selectivity. These populations differed dramatically, suggesting that DS cells may not contribute significantly to the synthesis of simple receptive fields: 1) whereas the first harmonic component (F1)-to-mean firing rate (F0) ratios of LGN DS cells are strongly nonlinear, those of simple cells are strongly linear; 2) whereas LGN DS cells have overlapped ON/OFF subfields, simple cells have either a single ON or OFF subfield or two spatially separate subfields; and 3) whereas the preferred directions of LGN DS cells are closely tied to the four cardinal directions, the directional preferences of simple cells are more evenly distributed. We further show that directional selectivity in LGN DS neurons is strongly enhanced by alertness via two mechanisms, 1) an increase in responses to stimulation in the preferred direction, and 2) an enhanced suppression of responses to stimuli moving in the null direction. Finally, our simulations show that these two consequences of alertness could each serve, in a vector-based population code, to hasten the computation of stimulus direction when rabbits become alert.