Finding the minimum column multiplicity for a bound set of variables is an important problem in Curtis decomposi-tion. To investigate this problem, we compared two graph-coloring programs: one exact, and another one based on heuristics which can give, however, provably exact results on some types of graphs. These programs were incorporated into the multi-valued decomposer MVGUD. We proved that the exact graph coloring is not necessary for high-quality functional decomposers. Thus we improved by orders of magnitude the speed of the column multiplicity problem, with very little or no sacrifice of decomposition quality. Comparison of our experimental results with competing de-composers shows that for nearly all benchmarks our solu-tions are best and time is usually not too high.