Predictive and multiresolution techniques for near-lossless image compression based on the criterion of maximum allowable deviation of pixel values are investigated. A procedure for near-lossless compression using a modification of lossless predictive coding techniques to satisfy the specified tolerance is described. Simulation results with modified versions of two of the best lossless predictive coding techniques known, CALIC and JPEG-LS, are provided. Application of lossless coding based on reversible transforms in conjunction with prequantization is shown to be inferior to predictive techniques for near-lossless compression. A partial embedding two-layer scheme is proposed in which an embedded multiresolution coder generates a lossy base layer, and a simple but effective context-based lossless coder codes the difference between the original image and the lossy reconstruction. Results show that this lossy plus near-lossless technique yields compression ratios close to those obtained with predictive techniques, while providing the feature of a partially embedded bit-stream.