Mixed-logit models are currently the state of the art in discrete-choice modelling, and their estimation in various forms (in particular, mixing revealed-preference and stated-preference data) is becoming increasingly popular. Although the theory behind these models is fairly simple, the practical problems associated with their estimation with empirical data are still relatively unknown and certainly not solved to everybody's satisfaction. In this paper we use a stated-preference dataset—previously used to derive willingness to pay for reduction in atmospheric pollution and subjective values of time—to estimate random parameter mixed logit models with different estimation methods. We use our results to discuss in some depth the problems associated with the derivation of willingness to pay with this class of models.