We propose the use of the singular value decomposition to decrease the storage required for wave function information. The specific case considered is determinantal full configuration interaction, but the same technique is readily applicable to truncated configuration interaction and coupled-cluster calculations of various types; as we discuss this is a reformulation of approximate methods that have been in use for some time, but our approach eliminates those approximations. Numerical examples support the contention that considerable compression of the wave function is possible without significant loss of accuracy: as expected a considerable amount of the information contained in the full CI wave function is redundant.