InfiniBand high performance networks require that the buffers used for sending or receiving data are registered. Since memory registration is an expensive operation, some communication libraries use caching (rcache) to amortize its cost, and copy data into pre-registered buffers for small messages. In this paper, we present a software protocol for InfiniBand that always uses a memory copy, and amortizes the cost of this copy with a superpipeline to overlap the memory copy and the RDMA. We propose a performance model of our protocol to study its behavior and optimize its parameters. We have implemented our protocol in the NewMadeleine communication library. The results of MPI benchmarks show a significant improvement in cache-unfriendly applications that do not reuse the same memory blocks all over the time, without degradation for cache-friendly applications.