A network (e.g., RSTP-based network) and method are described herein that can selectively eliminate latencies in the exchange of to-be-transmitted control messages (e.g., BPDUs) between bridges during the re/convergence of the network. The method includes a step of classifying to-be-transmitted control messages as either low-priority control messages or high-priority control messages. The method also has a step of limiting the transmission rate of the low-priority control messages in accordance with a traditional IEEE 802.1 RSTP. And, the method also includes a step of immediately transmitting the high-priority control messages that contain information that contributes to the re/convergence of the network.