What the basal ganglia do is an oft-asked question; answers range from the selection of actions to the specification of movement to the estimation of time. Here, I argue that the basal ganglia do what they do is a less-asked but equally important question. I show that the output regions of the basal ganglia create a stringent computational bottleneck, both structurally, because they have far fewer neurons than do their target regions, and dynamically, because of their tonic, inhibitory output. My proposed solution to this bottleneck is that the activity of an output neuron is setting the weight of a basis function, a function defined by that neuron's synaptic contacts. I illustrate how this may work in practice, allowing basal ganglia output to shift cortical dynamics and control eye movements via the superior colliculus. This solution can account for troubling issues in our understanding of the basal ganglia: why we see output neurons increasing their activity during behavior, rather than only decreasing as predicted by theories based on disinhibition, and why the output of the basal ganglia seems to have so many codes squashed into such a tiny region of the brain.