A queueing model with limited waiting room (buffer), mixed input traffic (Poisson and compound Poisson arrivals), and constant service rate is studied. Using average burst length, traffic intensity, and input-traffic mixture rate as parameters, we obtain relationships among buffer size, overflow probabilities, and expected message-queueing delay due to buffering. These relationships are portrayed on graphs that can be used as a guide in buffer design. Although this study arose in the design of statistical multiplexors, the queueing model developed is quite general and may be useful for other industrial applications.