Dichotomous-choice (referendum) contingent-valuation questions are inefficient in that a very large number of observations is required to identify a distribution of resource values with any degree of accuracy. An alternative questioning strategy introduces a follow-up dichotomous-choice question. We generalize upon previous analyses of this type of data by relaxing the assumption that the identical unobserved resource value motivates both responses. While values implied by the first and second responses are highly correlated and may be drawn from the same distribution, they are definitely not identical. Furthermore, assuming that they are can severely distort the estimated valuation distribution.