Two recent models of risky decision-making have emphasized the importance of a target return or a reference point in determining preferences and choices among gambles. Target returns and reference points represent variations on the concept of an aspiration level, an old idea in theories of decision-making. Additional evidence on the need to incorporate such a concept in the analysis of risky choice behavior is presented. In three experiments, the relationship of pairs of gambles to an assumed reference point was varied by adding or subtractng a constant amount from all outcomes. The results demonstrate that such translations of outcomes can result in the reversal of choice within pairs of gambles.