Generalized Multiprotocol Label Switching (GMPLS) is maturing to shape the next-generation mobile broadband IP networks, which will accommodate diverse technologies and various systems together. The Link Management Protocol (LMP), launched under the GMPLS context and being standardized by IETF, is designed for managing traffic-engineering (TE) links and verifying the reachability of control channels. A detailed study of the latest Internet-Draft on LMP has been conducted. Two important flaws in two of the four constituent procedures for LMP have been pointed out and improved by us in this paper. With regard to the link connectivity verification procedure, a batch-mode scheme is designed for enhancing its performance, scalability and flexibility, with theoretical analyses. In respect of the control channel management, a Privileged Hello Protocol is introduced to evade the dead-loop malfunction.