A method for treating Contingent Valuation data obtained from a polychotomous response format designed to accommodate respondent uncertainty is developed. The parameters that determine the probability of indefinite responses are estimated and used to truncate utility distributions within a structural model. The likelihood function for this model is derived, along with the posterior distributions that can be used for estimation within a Bayesian Monte Carlo Markov Chain framework. We use this model to examine two data sets and test a number of model related hypotheses. Our results are consistent with those from the psychology literature relating to uncertain response: a 'probable no' is more likely to suggest a defiite no, than a 'probable yes' is likely to suggest a definite yes. We also find that 'don't know' responses are context dependent. Comparing the performance of the methods developed in this paper with the ordered Probit which has been previously used in the literature with this type of data we find our methods outperform the ordered Probit for one of the data sets used.