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Tree-based routing protocols in low-rate wireless mesh networks usually have the detour problem in return for the no route discovery overhead. In this paper, we propose a novel algorithm, named Incremental Path Reduction (IPR), which incrementally shortens inefficient detoured path as more data packets are delivered. In IPR, data packets are delivered along the tree route in use by using 1-hop broadcast, enabling neighbor nodes to learn about the data packets' hop count. Using the hop counts, each node estimates their residual hop count to destination. As a result, each forwarder selects next hop node that has small residual hop count. In this way, IPR incrementally shortens the detoured route as more data packets are delivered. To verify our algorithm, we applied IPR to the representative tree routing protocols, and evaluated the path stretch and packet delivery ratio as well as control packet overhead. Simulation results show that IPR significantly enhances the overall routing metrics for any types of tree-based routing protocols.