Abstract —Goloboff recently introduced a method of character weighting that can be performed concomitantly with tree reconstruction. The basis for this method is his tree fitness measureF. The behaviour ofFis examined for a number of hypothetical and real data sets. It depends strongly on the value of the concavity constantk, and does not seem to be predictable. This makes it difficult to make general recommendations about the appropriate value ofkin specific cases. The basis forF, the number of extra steps taken by a character on a tree, does remain valuable as a basis for quality measures of trees, because it is independent of the number of states in the character, unlike the total number of steps and measures based on it such as CI and RC. Although no new measure is developed here, a number of requirements are formulated for an ideal tree quality measur