A new class of multistage interconnection networks is proposed. A network in this class consists of a standard multistage network, such as an omega network, augmented by multiplexers at the source nodes and demultiplexers at the destination. In addition, the first several stages are capable of adapting their routing decisions to avoid faults elsewhere in the network. The terminal reliability of this network is derived, and it is shown to have superior reliability, at a much lower cost than previous networks of similar fault tolerance. It is demonstrated that the proposed network's probability of acceptance, a common measure of performance for circuit-switched networks, is comparable to other networks of similar cost, but the greater number of paths it provides between source and destination should give it better performance under non-uniform traffic conditions.