One of the factors that can limit the scalability of MPI to exascale is the amount of memory consumed by the MPI implementation. In fact, some researchers believe that existing MPI implementations, if used unchanged, will themselves consume a large fraction of the available system memory at exascale. To investigate and address this issue, we undertook a study of the memory consumed by the MPICH2 implementation of MPI, with a focus on identifying parts of the code where the memory consumed per process scales linearly with the total number of processes. We report on the findings of this study and discuss ways to avoid the linear growth in memory consumption. We also describe specific optimizations that we implemented in MPICH2 to avoid this linear growth and present experimental results demonstrating the memory savings achieved and the impact on performance.