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Connection preemption plays an important role in multiclass QoS-aware networks. Most of the preemption research has focussed on the algorithms for choosing the appropriate set of preempted connections with minimal cost, in either a centralized or decentralized manner. In this paper, we introduce a new backward preemption policy for connection preemption. This policy reduces the number of redundant preemptions. We show how it can be integrated into the MPLS-TE (multiprotocol label switching-traffic engineering) framework. The policy can also be applied to other types of network control protocols with a two-way signaling process for setting up constraint-based routes with resource reservation. The proposed policy is also independent of the preemption decision algorithm and can work in both centralized and decentralized approaches. We examine the performance of the proposed approach by simulation studies.