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Optical burst switching (OBS) is a very promising switching technology for realization of an economical optical Internet. In OBS networks, when contention occurs at an intermediate switch, two or more bursts that are in contention can be lost because a forwarding path reservation is not made for a burst until a control message for the burst arrives. That is the reason why one of the critical design issues in OBS is finding ways to minimize burst dropping resulting from resource contention. In this paper, we propose and analyze a novel deflection routing protocol, which mitigates and resolves contention with significantly better performance as compared with techniques currently known in the literature. While several variants of the basic deflection routing scheme have been proposed before, they all lacked the ability to determine the alternate route based on clear performance objectives. In this paper, we present an on-demand deflection routing scheme, which sequentially performs the following: 1) based on certain performance criteria, dynamically determines if the burst should be deflection routed or retransmitted from source and 2) if the decision is to deflection route, then the same is done using a path that is based on minimization of a performance measure that combines distance and blocking due to contention. The proposed contention-based limited deflection routing scheme prevents injudicious deflection routing. Our simulation results show that the scheme proposed here has much superior performance both in terms of burst loss probability and increased network throughput. Through analytical and simulation modeling, a number of useful insights into the OBS network protocols and performance are provided.