In this paper we establish that a family of well-known normed compromise solutions for two-person claims problems respond appropriately to changes in the claims point. At the time of writing this paper, it was brought to my notice that Bossert (forthcoming) had independently obtained a similar result for a particular case of this family of solutions for claims problems with a larger number of agents. The extension of the general case to a larger number of agents is not however either immediate or obvious.