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This paper describes Extremely Opportunistic Routing (ExOR), a new unicast routing technique for multi-hop wireless networks. ExOR forwards each packet through a sequence of nodes, deferring the choice of each node in the sequence until after the previous node has transmitted the packet on its radio. ExOR then determines which node, of all the nodes that successfully received that transmission, is the node closest to the destination. That closest node transmits the packet. The result is that each hop moves the packet farther (or average) than the hops of the best possible pre-determined route.The ExOR design addresses the challenge of choosing a forwarding node after transmission using a distributed algorithm. First, when a node transmits a packet, it includes in the packet a simple schedule describing the priority order in which the potential receivers should forward the packet. The node computes the schedule based on shared measurements of inter-node delivery rates. ExOR then uses a distributed slotted MAC protocol for acknowledgements to ensure that the receivers agree who the highest priority receiver was.The efficacy of ExOR depends mainly on the rate at which the reception probability falls off with distance. Simulations based on measured radio characteristics [6] suggest that ExOR reduces the total number of transmissions by nearly a factor of two over the best possible pre-determined route.