Since the pioneering work of McFadden (1974), discretechoice random-utility models have become work horses in many areas in economics.In these models, the random variables enter additively or multiplicatively, and the noise distributions take a particular parametric form. We show that the same qualitative results, with closed-form choice probabilities, can be obtained for a wide class of distributions without such specifications. This class generalizes the statistically independent distributions where any two c.d.f.:s are powers of each others to a class that allows for statistical dependence, in a way analogous to how GEV distributions generalize Gumbel distributions. We show that this generalization is sufficient, and under statistical independence also necessary, for the following invariance property: all conditional random variables, when conditioning upon a certain alternative having been chosen, are identically distributed. In our general framework, proofs become simpler, more direct and transparent, well-known results are obtained as special cases, and one can characterize the Gumbel, Fréchet and Weibull distributions.