Allowing for variations in behaviour across respondents is one of the most fundamental principles in discrete choice modelling, given that the assumption of a purely homogeneous population cannot in general be seen to be valid. Two approaches have classically been used to address this problem; the use of deterministic segmentations of the population, and the use of a random continuous representation of variations in tastes across respondents. In this paper, a revised version of [10], we discuss an alternative approach, based on the use of discrete mixtures of underlying choice models over a finite set of distinct support points. The applied part of this paper shows how the resulting model structure can be used to test the validity of hypotheses such as the presence of individuals with zero valuations of travel-time changes.