An imposing number of lossy compression techniques used in medicine, represents a challenge for the developers of a Picture Archiving and Communication System (PACS). How to choose an appropriate lossy medical image compression technique for PACS? The question is not anymore whether to compress medical images in lossless or lossy way, but rather which type of lossy compression to use. The number of quality evaluations and criteria used for evaluation of a lossy compression technique is enormous. The mainstream quality evaluations and criteria can be broadly divided in two categories: objective and subjective. They evaluate the presentation (display) quality of a lossy compressed medical image. Also, there are few quality evaluations which measure technical characteristics of a lossy compression technique. In our opinion, technical evaluations represent an independent and invaluable category of quality evaluations. The conclusion is that quality evaluations from each category measure only one quality aspect of a medical image compression technique. Therefore, it is necessary to apply a representative(s) of each group to acquire the complete evaluation of lossy medical image compression technique for a PACS. Furthermore, a correlation function between the quality evaluation categories would simplify the overall evaluation of compression techniques. This would enable the use of medical images of highest quality while engaging the optimal processing, storage, and presentation resources. The paper represents a preliminary work, an introduction to future research and work aiming at developing a comprehensive quality evaluation system.