Uncertainty analyses and the reporting of their results can be misinterpreted when these analyses are conditional on a set of assumptions generally intended to bring some conservatism in the decisions. In this paper, two cases of conditional uncertainty analysis are examined. The first case includes studies that result, for instance, in a family of risk curves representing percentiles of the probability distribution of the future frequency of exceeding specified consequence levels conditional on a set of hypotheses. The second case involves analyses that result in an interval of outcomes estimated on the basis of conservative assumptions. Both types of results are difficult to use because they are sometimes misinterpreted as if they represented the output of a full uncertainty analysis. In the first case, the percentiles shown on each risk curve may be taken at face value when in reality (in marginal terms) they are lower if the chosen hypotheses are conservative. In the second case, the fact that some segments of the resulting interval are highly unlikely--or that some more benign segments outside the range of results are quite possible--does not appear. Also, these results are difficult to compare to those of analyses of other risks, possibly competing for the same risk management resources, and the decision criteria have to be adapted to the conservatism of the hypotheses. In this paper, the focus is on the first type (conditional risk curves) more than on the second and the discussion is illustrated by the case of the performance assessment of the Waste Isolation Pilot Plant in New Mexico. For policy-making purposes, however, the problems of interpretation, comparison, and use of the results are similar.