Selective Image Compression (SeLIC) is a compression technique where explicitly defined regions of interest (RoI) are compressed in a lossless way whereas image regions containing unimportant information are compressed in a lossy manner. Such techniques are of great interest in telemedicine or medical imaging applications with large storage requirements. In this paper we introduce and compare techniques with different functionalities. Moreover, we investigate the impact of using wavelet transforms and JPEG as underlying lossy compression algorithm.