Freedom from deadlock is a key issue in Cut-Through, Wormhole and Store and Forward networks, and such freedom is usually obtained through careful design of the routing algorithm. Most existing deadlock-free routing methods for irregular topologies do, however, impose severe limitations on the available routing paths. We present a method called Layered Routing, which gives rise to a series of routing algorithms, some of which perform considerably better than previous ones. Our method groups virtual channels into network layers, and to each layer it assigns a limited set of source/destination address pairs. This separation of traffic yields a significant increase in routing efficiency. We show how the method can be used to improve the performance of irregular networks, both through load balancing and by guaranteeing shortest-path routing. The method is simple to implement, and its application does not require any features in the switches other than the existence of a modest number of virtual channels. The performance of the approach is evaluated through extensive experiments within three classes of technologies. These experiments reveal a need for virtual channels as well as an improvement in throughput for each technology class.