Medical imaging technology has become essential for the improvement of medical practice. This led to advances in the technology, namely in image sampling resolutions, pixel bit-depth and inter slice resolution. Additionally, common use of medical images, the life expectancy of patients and legal restrictions led to increasing storage costs. Therefore, efficient compression of medical image data is in high demand, for archiving and transmission. In this work we propose to improve the compression efficiency of the Minimum Rate Predictors lossless encoder, by adding bi-directional prediction support and a histogram packing technique. The results show that the proposed method presents a higher compression efficiency than state-of-the-art HEVC encoder. The compression efficiency is improved by 20%, on average, when compared to HEVC and by 46.1% when compared with the original MRP algorithm.