This paper describes a highly efficient method for lossless compression of volumetric sets of medical images, such as CTs or MRIs. The proposed method, referred to as 3-D-MRP, is based on the principle of minimum rate predictors (MRPs), which is one of the state-of-the-art lossless compression technologies presented in the data compression literature. The main features of the proposed method include the use of 3-D predictors, 3-D-block octree partitioning and classification, volume-based optimization, and support for 16-b-depth images. Experimental results demonstrate the efficiency of the 3-D-MRP algorithm for the compression of volumetric sets of medical images, achieving gains above 15% and 12% for 8- and 16-bit-depth contents, respectively, when compared with JPEG-LS, JPEG2000, CALIC, and HEVC, as well as other proposals based on the MRP algorithm.