The use of multifocal-plane, time-lapse recordings of living specimens has allowed investigators to visualize dynamic events both within ensembles of cells and individual cells. Recordings of such four-dimensional (4D) data from digital optical sectioning microscopy produce very large data sets. We describe a wavelet-based data compression algorithm that capitalizes on the inherent redunancies within multidimensional data to achieve higher compression levels than can be obtained from single images. The algorithm will permit remote users to roam through large 4D data sets using communication channels of modest bandwidth at high speed. This will allow animation to be used as a powerful aid to visualizing dynamic changes in three-dimensional structures.