Methods of lossless compression of medical image data are considered. Selected class of efficient algorithms have been constructed, examined, and optimized to conclude the most useful tools for medical image archiving and transmission. Image data scanning, 2D context-based prediction and interpolation, and statistical models of entropy coder have been optimized to compress effectively ultrasound (US), magnetic resonance (MR), and computed tomography (CT) images. The SSM technique of suitable data decomposing scanning method followed by probabilistic modeling of the context in arithmetic encoding have occurred the most useful in our experiments. Context order, shape, and alphabet have been fitted to local data characteristics to decrease image data correlation and dilution of statistical model. Average bit rate value over test images is equal to 2.53 bpp for SSM coder and significantly overcomes 2.92 bpp of CALIC bit rate. Moreover, optimization of lossless wavelet coder by thinking of efficient subband decomposition schemes, and integer-to-integer transforms is reported. Efficient hybrid coding method (SHEC) as a complete tool for medical image archiving and transmission is proposed. SHEC develops SSM by including CALIC-like coder to compress the highest quality images and JPEG2000 wavelet coder for progressive delivering of high and middle quality images in telemedicine systems.