The telencephalic premotor nucleus HVC is situated at a critical point in the pattern-generating premotor circuitry of oscine songbirds. A striking feature of HVC's premotor activity is that its projection neurons burst extremely sparsely. Here we present a computational model of HVC embodying several central hypotheses: 1) sparse bursting is generated in bistable groups of recurrently connected robust nucleus of the arcopallium (RA)-projecting (HVCRA) neurons; 2) inhibitory interneurons terminate bursts in the HVCRA groups; and 3) sparse sequences of bursts are generated by the propagation of waves of bursting activity along networks of HVCRA neurons. Our model of sparse bursting places HVC in the context of central pattern generators and cortical networks using inhibition, recurrent excitation, and bistability. Importantly, the unintuitive result that inhibitory interneurons can precisely terminate the bursts of HVCRA groups while showing relatively sustained activity throughout the song is made possible by a specific constraint on their connectivity. We use the model to make novel predictions that can be tested experimentally.