Ambiguity is uncertainty about an option's outcome-generating process, and is characterized as uncertainty about an option's outcome probabilities. Subjects, in choice tasks, typically have avoided ambiguous options. Descriptive models are identified and tested in two studies which had subjects rank monetary lotteries according to preference. In Study 1, lotteries involved receiving a positive amount or nothing, where P denotes the probability of receiving the nonzero amount. Subjects were willing to forego expected winnings to avoid ambiguity near P = .50 and P = .75. Near P = .25, a significant percentage of subjects exhibited ambiguity seeking, with subjects, on average, willing to forego expected winnings to have the more ambiguous option. The observed behavior contradicts the viability of a proposed lexicographic model. Study 2 tested four polynomial models using diagnostic properties in the context of conjoint measurement theory. The results supported a sign dependence of ambiguity with respect to the probability level P, such that subjects' preference orderings over ambiguity reversed with changes in P. This behavior was inconsistent with all the three-factor polynomial models investigated. Further analyses failed to support a variant of portfolio theory, as well. The implications of these results for the descriptive modeling of choice under ambiguity are discussed.