In this paper we propose a wavelet based method for compressing volumetric data with little loss in quality allowing fast random access to individual voxels within the volume. Such a method is important since storing and visualizing very large volumes impose heavy demands on internal memory and external storage facilities, a problem not likely to become less in the future, making it accessible only to users with huge and expensive computers. Experimental results on the CT data-set of the Visible Human have shown that our method provides very high compression rates with fairly fast random access.