As we continue toward exascale, scientific data volume is continuing to scale and becoming more burdensome to manage. In this paper, we lay out opportunities to enhance state of the art data management techniques. We emphasize well-principled data compression, and using it to achieve progressive refinement. This can both accelerate I/O and afford the user increased flexibility when she interacts with the data. The formulation naturally maps onto enabling partitioning of the progressively improving-quality representations of a data quantity into different media-type destinations, to keep the highest priority information as close as possible to the computation, and take advantage of deepening memory/storage hierarchies in ways not previously possible. Careful monitoring is requisite to our vision, not only to verify that compression has not eliminated salient features in the data, but also to better understand the performance of massively parallel scientific applications. Increased mathematical rigor would be ideal,to help bring compression on a better-understood theoretical footing, closer to the relevant scientific theory, more aware of constraints imposed by the science, and more tightly error-controlled. Throughout, we highlight pathfinding research we have begun exploring related these topics, and comment toward future work that will be needed.