This paper analyses data from a contingent valuation experiment carried out in a context with large degree of preference heterogeneity and valuation ambiguity. Despite this challenge, by implementing estimation of an unrestricted valuation function on pooled data from two elicitation formats, utilizing all preference information available from the survey, we are able to estimate welfare measures with an acceptable degree of statistical confidence. It turns out that an offshore wind farm, a priori believed to constitute a bad that people would be willing to pay to avoid, instead was a good that people would be willing to forego under compensation. This was true on average but not for all study participants. Two key determinants of preferences were spatial proximity to the proposed wind farm and perceptions of the visual impacts of wind turbines. Individuals who would be near and thought wind turbines are “ugly” had a mean willingness to pay to avoid the wind farm of about $508 per household per year. In contrast, those who would be far away and perceived wind turbines to be “beautiful” had a negative mean willingness to pay to avoid the wind farm of about −$595 per household per year.