One of the more exasperating features of orbital-based electronic structure calculations is that correlated wave functions involve many terms. This requires considerable storage in a computer, and inhibits, or at least makes very intricate, parallel implementations of large coupled-cluster or configuration interaction (CI) calculations because of the data motion necessitated. At the same time, the information carried in such wave functions involves considerable redundancy, and we have begun to explore how techniques for data compression can be employed to analyze this redundancy, and perhaps to lead not only to a very compact representation of correlated wave functions, but also to improved parallelism and performance by greatly reducing or even eliminating data motion. In this talk I will give a very general overview of our approach so far, illustrating it with several examples of full CI calculations, and linking it to other approaches. Although our experience is preliminary, the approach shows considerable promise.