A method for communication includes configuring a plurality of ring nodes to communicate over a communication network that includes two or more overlapping communication rings, each ring including two unidirectional ringlets in mutually-opposite directions. A data packet including one or more header fields is accepted at an ingress ring node. An egress ring node to which the data packet is to be forwarded by the ingress ring node is determined. A subset of the rings including one or more common rings that are connected to both the ingress and egress ring nodes is identified. A ringlet of a ring among the one or more common rings is selected responsively to a respective value of at least one of the header fields of the packet. The data packet is forwarded from the ingress ring node to the egress ring node over the selected ringlet.