Lossy compression algorithms enable the efficient transmission of large medical image datasets over bandwidth-limited digital networks or facilitate the long-term storage of the daily image production. Although JPEG 2000 has been adopted by DICOM as the standard for lossy-to-lossless compression, still a set of guidelines needs to be derived that allows for the usage of the lossy mode, potentially jeopardizing the accuracy of lesion detection and characterization, and so, of the resulting diagnosis task effectiveness in the medical diagnosis process. In this article the authors present and evaluate a generic methodology for the determination of the minimal bit rate that still ensures an accurate detection in magnetic resonance images of specific lesions. In this article, they demonstrate the methodology for two particular pathologies, i.e., multiple sclerosis and Virchow-Robin space enlargements. Involving qualified personnel, the minimal bit rate is estimated from ROC experiments initially simulated through mathematical observers that are designed with several objective metrics. The mathematical observer models included three variants of the Hotelling observer plus the non-prewhitening matched filter with eye model, while the objective measures are based on distance, correlation, singular value decomposition, and structural similarity. The results indicate that the highest compression without seriously affecting the detection of the studied lesions is achieved at a bit rate of 0.125 bpp. At this value, the detection effectiveness exceeded 95% with less than 5% standard deviation, while only 4.4% of the outcomes were classified as false negatives by the experts and 11.6% as false positives. The optimal bit rate found assures that important information on the small investigated structures is still preserved for their accurate detection and their a posteriori characterization.