The standard counter-examples to Luce's choice axioms involve similarities between some of the choice alternatives. If one regards choice as a random utility process then the similarities can be interpreted as correlation between the utility variables; the counter-examples are then simply explained. A class of multivariate double exponential distributions is discussed which modifies Luce's probability formula to allow for similarities. The choice by features model proposed here defines one way in which several features, or similarity groupings, may be combined. An important special case of the model is an extension of Luce's to account for similarities; this model can be parameterized in a natural way, and it is then possible to estimate and test hypotheses about the parameters of interest.