This paper deals with the problem of reroute sequence planning for label switched paths (LSPs) in multiprotocol label switching (MPLS) networks. This problem arises when the path set is recalculated by a global optimization method for achieving a better resource utilization. In this case we have to find a sequence of the one-by-one reconfiguration of the LSPs from their original paths to the optimized paths, with the constraint that the link capacities should not be violated at any time during the reroute process. The problem is computationally hard in real-world situations because of the large amount of routers and LSPs in the network, so that neither exact nor approximation algorithms have practical relevance. We introduce a number of heuristic approaches, which are investigated through extensive empirical tests based on real network topologies. The results reveal the complexity of the problem. We propose possible solutions and suggest future research directions for alternative answers to the reroute sequence planning.