Linear predictive techniques perform poorly when used with color-mapped images where pixel values represent indices that point to color values in a look-up table. Reordering the color table, however, can lead to a lower entropy of prediction errors. In this paper, we investigate the problem of ordering the color table such that the absolute sum of prediction errors is minimized. The problem turns out to be intractable, even for the simple case of one-dimensional (1-D) prediction schemes. We give two heuristic solutions for the problem and use them for ordering the color table prior to encoding the image by lossless predictive techniques. We demonstrate that significant improvements in actual bit rates can be achieved over dictionary-based coding schemes that are commonly employed for color-mapped images.