We propose a fully three-dimensional wavelet-based coding system featuring 3D encoding/2D decoding functionalities. A fully three-dimensional transform is combined with context adaptive arithmetic coding; 2D decoding is enabled by encoding every 2D subband image independently. The system allows a finely graded up to lossless quality scalability on any 2D image of the dataset. Fast access to 2D images is obtained by decoding only the corresponding information thus avoiding the reconstruction of the entire volume. The performance has been evaluated on a set of volumetric data and compared to that provided by other 3D as well as 2D coding systems. Results show a substantial improvement in coding efficiency (up to 33%) on volumes featuring good correlation properties along the z axis. Even though we did not address the complexity issue, we expect a decoding time of the order of one second/image after optimization. In summary, the proposed 3D/2D Multidimensional Layered Zero Coding System (3D/2D MLZC) provides the improvement in compression efficiency attainable with 3D systems without sacrificing the effectiveness in accessing the single images characteristic of 2D ones.