We present a general purpose lossless greyscale image compression method, TMW, that is based on the use of linear predictors and implicit segmentation. We then proceed to extend the presented methods to cover near lossless image compression. In order to achieve competitive compression, the compression process is split into an analysis step and a coding step. In the first step, a set of linear predictors and other parameters suitable for the image is calculated, which is included in the compressed file and subsequently used for the coding step. This adaption allows TMW to perform well over a very wide range of image types. Other significant features of TMW are the use of a one-parameter probability distribution, probability calculations based on unquantized prediction values, blending of multiple probability distributions instead of prediction values, and implicit image segmentation. For lossless image compression, the method has been compared to CALIC on a selection of test images, and typically outperforms it by between 2 and 10 percent. For near lossless image compression, the method has been compared to LOCO (Weinberger et al. 1996). Especially for larger allowed deviations from the original image the proposed method can significantly outperform LOCO. In both cases the improvement in compression is achieved at the cost of considerably higher computational complexity.