The Auckland Police Communication Centre accepts both emergency and some non-emergency calls from the upper half of the North Island, and dispatches police units to those calls. The centre would like to select staffing levels so that certain customer service performance criteria are met. We investigate the use of queuing models to assist in setting these staffing levels. An approach that ignores the fact that emergency calls receive higher priority (the standard Erlang delay formula) tends to yield slightly higher staffing levels than a second approach that explicitly considers the two priority levels of the calls. The existing shift structures at the centre are perhaps not as flexible as one might like to deal with variable demand. With smaller shift lengths, and more flexible starting times, one would expect to need less staff to cover the required levels, and our analysis supports this.