Vasopressin secreting neurons of the rat hypothalamus discharge lengthy, repeating bursts of action potentials in response to physiological stress. Although many electrical currents and calcium-dependent processes have been isolated and analyzed in these cells, their interactions are less well fathomed. In particular, the mechanism of how each burst is triggered, sustained, and terminated is poorly understood. We present a mathematical model for the bursting mechanism, and we support our model with new simultaneous electrical recording and calcium imaging data. We show that bursts can be initiated by spike-dependent calcium influx, and we propose that the resulting elevation of bulk calcium inhibits a persistent potassium current. This inhibition depolarizes the cell above threshold and so triggers regenerative spiking and further calcium influx. We present imaging data to show that bulk calcium reaches a plateau within the first few seconds of the burst, and our model indicates that this plateau occurs when calcium influx is balanced by efflux and uptake into stores. We conjecture that the burst is terminated by a slow, progressive desensitization to calcium of the potassium leak current. Finally, we propose that the opioid dynorphin, which is known to be secreted from the somatodendritic region and has been shown previously to regulate burst length and phasic activity in these cells, is the autocrine messenger for this desensitization.