Volume data sets resulting from, e.g., computerized tomography (CT) or magnetic resonance (MR) imaging modalities require enormous storage capacity even at moderate resolution levels. Such large files may require compression for processing in CPU memory which, however, comes at the cost of decoding times and some loss in reconstruction quality with respect to the original data. For many typical volume visualization applications (rendering of volume slices, subvolumes of interest, or isosurfaces) only a part of the volume data needs to be decoded. Thus, efficient compression techniques are needed that provide random access and rapid decompression of arbitrary parts the volume data. We propose a technique which is block based and operates in the wavelet transformed domain. We report performance results which compare favorably with previously published methods yielding large reconstruction quality gains from about 6 to 12 dB in PSNR for a5123 ‐volume extracted from the Visible Human data set. In terms of compression our algorithm compressed the data 6 times as much as the previous state‐of‐the‐art block based coder for a given PSNR quality.