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The size of standard volumetric data sets in medical imaging is rapidly increasing causing severe performance limitations in direct volume rendering pipelines. The methods presented in this paper exploit the medical knowledge embedded in the transfer function to reduce the required bandwidth in the pipeline. Typically, medical transfer functions cause large subsets of the volume to give little or no contribution to the rendered image. Thus, parts of the volume can be represented at low resolution while retaining overall visual quality. This paper introduces the use of transfer functions at decompression time to guide a level-of-detail selection scheme. The method may be used in combination with traditional lossy or lossless compression schemes. We base our current implementation on a multi-resolution data representation using compressed wavelet transformed blocks. The presented results using the adaptive decompression demonstrate a significant reduction in the required amount of data while maintaining rendering quality. Even though the focus of this paper is medical imaging, the results are applicable to volume rendering in many other domains.