In many non-market valuation settings stakeholders will be uncertain as to their exact willingness-to-pay for a proposed environmental amenity. It then makes sense for the analyst to treat this value as a random variable with distribution only known to the respondent. In stated preference settings, researchers have used elicitation formats with multiple bids and uncertain-response options to learn about individual value distributions. Past efforts have focused on inference involving the expectation of individual densities. This requires stringent and likely unrealistic assumptions regarding the shape or moments of individual value distributions. We propose a Latent Thresholds Estimator that focuses instead on the range, i.e. minimum and maximum willingness-to-pay of individual respondents. The estimator efficiently exploits correlation patterns in individual responses and does not require any restrictive assumptions on underlying values. It also nests some of the existing approaches, which are not statistically supported for our empirical application. Copyright 2012, Oxford University Press.