Medical images are very important for diagnostics and therapy. However, digital imaging generates large amounts of data which need to be compressed, without loss of relevant information, to economize storage space and allow speedy transfer. In this research three techniques are implemented for medical image compression, which provide high compression ratios with no loss of diagnostic quality. Different image modalities are employed for experiments in which X-rays, MRI, CT scans, Ultrasounds and Angiograms are included. The proposed schemes are evaluated by comparing with existing standard compression techniques like JPEG, lossless JPEG2000, LOCOI and Huffman Coding. In a medical image only a small region is diagnostically relevant while the remaining image is much less important. This is called Region of Interest (ROI). The first approach compresses the ROI strictly losslessly and the remaining regions of the image with some loss. In the second approach an image is first compressed at a high compression ratio but with loss, and the difference image is then compressed losslessly. Difference image contain less data and is compressed more compactly than original. Third approach exploits inter-image redundancy for similar modality and same part of human body. More similarity means less entropy which leads to higher compression performance. The overall compression ratio is combination of lossy and lossless compression ratios. The resulting compression is not only strictly lossless, but also expected to yield a high compression ratio. These techniques are based on self designed Neural Network Vector Quantizer (NNVQ) and Huffman coding. Their clever combination is used to get lossless effect. These are spatial domain techniques and do not require frequency domain transformation. i An overall compression ratio of 6-14 is obtained for images with proposed methods. Whereas, by compressing same images by a lossless JPEG2K and Huffman, compression ratio of 2 is obtained at most. The main contribution of the research is higher compression ratios than standard techniques in lossless scenario. This result will be of great importance for data management in a hospital and for teleradiology.