The Resource Reservation Protocol for Traffic Engineering (RSVP-TE) must recover its state after a control plane failure so that the established connections in the data plane continue to be provided full services, are not disrupted by new connection setup requests, and survive any data plane failures. We outline the RSVP-TE Graceful Restart (GR) mechanism defined by the IETF. In this paper, we provide a comprehensive survey of the information that may be carried by RSVP-TE signaling messages when a connection is to be established and the state information that is stored in an RSVP-TE signaling module. We then propose an enhancement for RSVP-TE GR to alleviate the requirement of local recovery of the data plane state. Our proposal includes a two-step RSVP-TE state recovery, which uses a fast recovery to recover the RSVP-TE state in which labels were idle before a control plane failure and a detailed recovery to recover all of the RSVP-TE state. The fast RSVP-TE state recovery is realized as an extension to the RSVP-TE Hello mechanism, allowing a restarting node to process new connection setup requests as quickly as possible without interfering with existing connections. The detailed RSVP-TE state recovery generally follows RSVP-TE GR with minor modifications that can be performed in the background in parallel with normal RSVP-TE operations for connection setup and removal. Our performance evaluations show that our proposal shortens the waiting time for new connection setups being processed by a restarting node.