Label switch paths (LSP) are regarded as the routing components of an end-to-end connection in label switching network from the traffic engineering point of view. Thus, an end-to-end connection may travel more than one LSP. The QoS of this end-to-end connection relies on the performance of each LSP it travels. Therefore, to carefully arrange LSP is an essential step towards QoS networks. Generally speaking, the capacity of a specific link is not allocated for high-priority LSP because it will cause inflexibility in the scheduling process. In this paper, the best-fit shortest path (BSP) assignment and the worst shortest path (WSP) assignment schemes are proposed for the arrangement of label switch paths. In order to provide flexibility in packet scheduling, we propose that the BSP scheme to be applied for allocation of low-priority LSP and the WSP scheme is used for the arrangement of LSP with high priority. Based on these two schemes, we extend them with elastic bandwidth allocation to prevent the bandwidth of the link from being occupied by the higher priority LSP. The experimental results indicate that, compared to the BSP-only scheme, the proposed hybrid scheme demonstrates a more efficient way of arranging prioritized LSP. Moreover, the proposed elastic constrained bandwidth allocation scheme also illustrates a rather good performance in smoothing the link utilization of high-priority LSP.