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Multipath traffic engineering has been studied to disperse traffic flows on an IP network and guarantee end-to-end quality of service. We propose to apply k shortest simple paths as the multiple paths between an edge and the center router of a network and also try to disperse the traffic between them. The new heuristic k shortest simple path algorithm proposed in this paper is called k-shortest paths first (k-SPF), and it creates k shortest simple paths faster than the conventional Yen's algorithm does. In addition, we will make it clear that applying k shortest simple paths is not sufficient for further dispersing traffic flows without making bottleneck links that lack available bandwidth. To solve this problem, we propose to change the values of the parameters of k-SPF. We show that this change of parameters effectively achieves appropriate traffic dispersion without making any bottleneck links. We also show that this change does not require many path candidates to be used in k-SPF, so k-SPF processing time becomes drastically shorter.