Input buffered switches with Virtual Output Queueing (VOQ) can be unstable when presented with unbalanced loads. Existing scheduling algorithms, including iSLIP for Input Queued (IQ) switches and Round Robin (RR) for Combined Input and Crossbar Queued (CICQ) switches, exhibit instability for some schedulable loads. We investigate the use of a queue length threshold and bursting mechanism to achieve stability without requiring internal speed-up. An analytical model is developed to prove that the burst stabilization protocol achieves stability and to predict the minimum burst value needed as a function of offered load. The analytical model is shown to have very good agreement with simulation results. These results show the advantage of the RR/RR CICQ switch as a contender for the next generation of high-speed switches.