Destination choice models with individual-specific taste variation have become the presumptive analytical approach in applied nonmarket valuation. Under the usual specification, tastes are represented by coefficients of site attributes that enter utility, and the distribution of these coefficients is estimated. The distribution of willingness-to-pay (WTP) for site attributes is then derived from the estimated distribution of coefficients. Though conceptually appealing this procedure often results in untenable distributions of willingness to pay. An alternative procedure is to estimate the distribution of willingness to pay directly, through a re-parameterization of the model. We compare hierarchical Bayes and maximum simulated likelihood estimates under both approaches, using data on site choice in the Alps. We find that models parameterized in terms of WTP provide more reasonable estimates for the distribution of WTP, and also fit the data better than models parameterized in terms of attribute coefficients. This approach to parameterizing utility is hence deemed promising for applied nonmarket valuation.