In two experiments, we demonstrate that despite indicating indifference when probed about risk or delay in isolation, when forced to explicitly trade‐off between the two, participants prefer delayed over risky rewards. This pattern of findings sets a boundary condition for any common utility‐based comparison process involving both risk and delay. Furthermore, this change from indifference‐in‐isolation to delay‐preference‐in‐a‐trade‐off strengthens as reward amount increases. Exploratory modeling results suggest that the shift in preference can be explained by allowing for different discount rates for delay‐only choices compared with when delay is in competition with risk. This explanation is better than one in which probability weighting is different between risk‐only choices and risks considered in the presence of a delay. Together, the empirical and modeling work lays a path for future investigations of why and when people's evaluation of the properties of risky and delayed choices vary as a function of the alternatives on offer. Copyright © 2017 John Wiley & Sons, Ltd.