Avian brain area HVC is known to be important for the production of birdsong. In zebra finches, each RA-projecting neuron in HVC emits a single burst of spikes during a song motif. The population of neurons is activated in a precisely timed, stereotyped sequence. We propose a model of these burst sequences that relies on two hypotheses. First, we hypothesize that the sequential order of bursting is reflected in the excitatory synaptic connections between neurons. Second, we propose that the neurons are intrinsically bursting, so that burst duration is set by cellular properties. Our model generates burst sequences similar to those observed in HVC. If intrinsic bursting is removed from the model, burst sequences can also be produced. However, they require more fine-tuning of synaptic strengths, and are therefore less robust. In our model, intrinsic bursting is caused by dendritic calcium spikes, and strong spike frequency adaptation in the soma contributes to burst termination.