Message Passing Interface (MPI) point-to-point communications are usually realized with two protocols, the eager protocol for small messages and the rendezvous protocol for medium and large sized messages. Traditional senderinitiated rendezvous protocols are sub-optimal in many situations. In this work, we propose to refine the rendezvous protocol for medium and large messages on RDMA-enabled clusters with three protocols that are customized for different situations, a hybrid protocol for medium sized messages when the sender arrives early, a sender-initiated protocol for large messages when the sender arrives early, and a receiver-initiated protocol when the receiver arrives early. In comparison to traditional sender-initiated rendezvous protocols, the proposed scheme reduces unnecessary synchronizations, decreases the number of control messages that are in the critical path of communications, and improves the communication progress, which results in a significantly better communication-computation overlap capability. We present and analyze these protocols, and describe how these protocols and the eager protocol can be seamlessly integrated in one system without introducing an excessive number of control messages. We have implemented the proposed scheme for InfiniBand clusters. The experimental results demonstrate the effectiveness of the proposed technique.