Experimental evidence suggests that individuals are more risk averse when they perceive risk that is gradually resolved over time. We address these findings by studying a decision maker who has recursive, nonexpected utility preferences over compound lotteries. The decision maker has preferences for one-shot resolution of uncertainty if he always prefers any compound lottery to be resolved in a single stage. We establish an equivalence between dynamic preferences for one-shot resolution of uncertainty and static preferences that are identified with commonly observed behavior in Allais-type experiments. The implications of this equivalence on preferences over information systems are examined. We define the gradual resolution premium and demonstrate its magnifying effect when combined with the usual risk premium.