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The increase in real-time applications such as voice over IP, audio and video streaming in the public Internet has warranted QoS based routing. But today's Internet largely supports best effort traffic. Thus, a QoS routing in the best effort environment is required to support real-time applications. Flooding of some QoS attributes (e.g. available bandwidth) has been used for QoS routing. But we believe a better way of implementing QoS routing is to localize the QoS routing changes to the region where QoS has deteriorated, instead of flooding the entire network. We present a load sensitive routing (LSR) algorithm that tries to route packets through an alternate path when congestion is reported on a link. LSR routing is contained locally i.e. only the neighboring nodes of a congested node perform LSR routing. Hence it has much less overhead than other QoS routing protocols reported. The LSR algorithm is designed carefully to avoid any looping. We have simulation results of the LSR algorithm which show its average performance to be better than the OSPF algorithm in terms of delay and jitter.