We propose a new high-performance message router for k-ary n-cube multicomputer systems, called the Tokky router. The router utilizes a small number of queues at the outputs of its communication ports to allow fully adaptive routing, misrouting to prevent deadlocks and randomization to prevent livelock. Uncongeste network performance is improved by the inclusion of the packet expressway. Accurate models are developed to predict the switch and buffer performance of routers for varying radix and dimension and these models can be used in the design of routers for networks other than those investigated here. The simulated performance of the router exceeds that of published results for oblivious routers and is equal to or exceeds those reported for other adaptive routers. These performance predictions are especially encouraging when the simplicity of the control structures required to implement the router are taken into consideration.