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In IEEE 802.11-based wireless mesh networks, routing is crucial in achieving high throughput in face of both interflow and intra-flow interference. Prior work focuses on finding the maximum available bandwidth path when a new flow enters the network. However, few has considered the effect of the new flow on the throughput of the existing flows. We propose a routing framework that uses the topology map of a mesh network with the carrier sense and interference relations and estimates the available bandwidth of a candidate path. We propose two algorithms for finding a route for a new flow: (1) FIRM searches for the maximum bandwidth path for the new flow, and (2) FIRM+ not only considers the available bandwidth of a path for the new flow, but also the amount of throughput degradation of existing flows. We implement and evaluate FIRM and FIRM+ with the IRU routing algorithm on a 15 node indoor IEEE 802.11a testbed. Various experiments reveal that FIRM+ achieves the highest total throughput of all flows.