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Combined input-crosspoint buffered (CICB) switches can achieve high switching performance without speedup. However, the dedicated crosspoint buffers in a CICB switch may not be efficiently used, and throughput degradation may occur. This throughput degradation is especially observable under flows with high data rates and long distances between the line cards and the buffered crossbar. This paper introduces two load-balanced CICB switches: the load-balancing CICB switch with full access (LB-CICB-FA) and the load-balancing CICB switch with single access (LB-CICB-SA). The proposed switches use the crosspoint buffers efficiently and support long distances between the line cards and buffered crossbar with crosspoint buffers smaller than those in a CICB switch by a factor of N, where N is the number of ports. It is proven that the LB-CICB-FA switch with random selection of the configuration of the load-balancing stage, input queues, and crosspoint queues is weakly stable under admissible independent and identical distributed (i.i.d.) traffic. Additional simulation results support the correctness of the theoretical analysis. Furthermore, it is shown that the throughput of the LB-CICB-SA switch with the longest-queue first (LQF) and first-come first-served (FCFS) as input and output arbitrations, respectively, is 100% under admissible i.i.d. traffic. The proposed switches keep cells in sequence and use no speedup. The low implementation complexity of the load-balancing stage is discussed and shown to be small.