A simple model was proposed to account for the direction selectivity of neurons in the primary visual cortex, area V1. In this model, the temporal asymmetries in the summation of inhibition and excitation that produce directionality were generated by structural asymmetries in the tangential organization of the basal dendritic tree of cortical neurons. We reconstructed dendritic trees of neurons with known direction preferences and found no correlation between the small biases of a neuron’s dendritic morphology and its direction preference. Detailed simulations indicated that even when the electrotonic asymmetries in the dendrites were extreme, as in cortical Meynert cells, the biophysical properties of single neurons could contribute only partially to the directionality of cortical neurons.