This paper focuses on lossless medical image compression methods for 3D volumetric medical images that operate on three-dimensional (3D) reversible integer wavelet transforms. We offer an application of the Set Partitioning in Hierarchical Trees (SPIHT) algorithm to volumetric medical images, using a 3D wavelet decomposition and a 3D spatial dependence tree. The wavelet decomposition is accomplished with integer wavelet filters implemented with the lifting method, where careful scaling and truncations keep the integer precision small and the transform unitary. We have tested our encoder on volumetric medical images using different integer filters and different coding unit sizes. The coding unit sizes of 16 and 8 slices save considerable memory and coding delay from full sequence coding units used in previous works. Results show that, even with these small coding units, our algorithm with certain filters performs as well and sometimes better in lossless coding than previously coding systems using 3D integer wavelet transforms on volumetric medical images.