Advances in computed tomography (CT) have resulted in a substantial increase in the size of datasets. We built a new concept of medical image compression that provides the best compromise between compression rate and image quality. The method is based on multiple contexts and regions-of-interest (ROI) defined according to the degree of clinical interest. High priority areas (primary ROIs) are assigned a lossless compression. Other areas (secondary ROIs and background) are compressed with moderate or heavy losses. The method is applied to a whole dataset of CT angiography (CTA) of the lower extremity vasculature. It is compared to standard lossy compression techniques in terms of quantitative and qualitative image quality. It is also compared to standard lossless compression techniques in terms of image size reduction and compression ratio. The proposed compression method met quantitative criteria for high-quality encoding. It obtained the highest qualitative image quality rating score, with a statistically significant difference compared to other methods. The average compressed image size was up to 61% lower compared to standard compression techniques, with a 9:1 compression ratio compared with original non-compressed images. Our new adaptive 3D compression method for CT images can save data storage space while preserving clinically relevant information.