Uncovering the roles of neural feedback in the brain is an active area of experimental research. In songbirds, the telencephalic premotor nucleus HVC receives neural feedback from both forebrain and brainstem areas. Here we present a computational model of birdsong sequencing that incorporates HVC and associated nuclei and builds on the model of sparse bursting presented in our preceding companion paper. Our model embodies the hypotheses that (1) different networks in HVC control different syllables or notes of birdsong, (2) interneurons in HVC not only participate in sparse bursting but also provide mutual inhibition between networks controlling syllables or notes, and (3) these syllable networks are sequentially excited by neural feedback via the brainstem and the afferent thalamic nucleus Uva, or a similar feedback pathway. We discuss the model's ability to unify physiological, behavioral, and lesion results, and we use it to make novel predictions that can be tested experimentally. The model suggests a neural basis for sequence variations, shows that stimulation in the feedback pathway may have different effects depending on the balance of excitation and inhibition at the input to HVC from Uva, and predicts deviations from uniform expansion of syllables and gaps during HVC cooling.