In the paper “On the nucleolus of the basic vehicle routing game”, Mathematical Programming 72, 83–100 (1996), Göthe-Lundgren et al. develop a constraint generation method to compute the pre-nucleolus of a game. Their method assumes that constraints that are redundant in the representation of the core can be ignored in the computation of the pre-nucleolus. We provide an example that shows that for a game with an empty core such an assumption is, in general, not valid. Further, we show that a statement made by Göthe-Lundgren et al. about an intuitive interpretation of the pre-nucleolus is misleading.