This paper provides an in-depth analysis of the software overheads in the MPI performance-critical path and exposes mandatory performance overheads that are unavoidable based on the MPI-3.1 specification. We first present a highly optimized implementation of the MPI-3.1 standard in which the communication stack---all the way from the application to the low-level network communication API---takes only a few tens of instructions. We carefully study these instructions and analyze the root cause of the overheads based on specific requirements from the MPI standard that are unavoidable under the current MPI standard. We recommend potential changes to the MPI standard that can minimize these overheads. Our experimental results on a variety of network architectures and applications demonstrate significant benefits from our proposed changes.