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. Re-ordering 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 1D prediction schemes. We given two heuristic solutions for the problem and use them for ordering the color table prior to encoding the image by lossless DPCM like techniques. The first heuristic is based on a simulated annealing approach and is computationally expensive. The second heuristic, however, is simple and sacrifices optimality for computational efficiency. It involves successive merging of ordered sets of color table entries until all the entries have been merged into a single set. Simulation results giving comparison of the two heuristics with previous approaches are presented. It is seen that significant improvements can be obtained with the proposed heuristics. We then use a simple error modeling technique to encode prediction residuals and demonstrate the improvements in actual bit rates that can be achieved over dictionary based coding schemes that are commonly employed for color-mapped images.