Research on delay discounting and inter‐temporal choice has yielded significant insights into decision making. Although research has focused on delayed gains, the discounting of losses is potentially important in precisely those areas where the discounting of gains has proved informative (e.g., substance use and abuse). Participants in the current study completed both a questionnaire consisting of choices between immediate and delayed gains and an analogous questionnaire consisting of choices between immediate and delayed losses. For almost all participants, the likelihood of choosing the delayed gain decreased with increases in the wait until it would be received. In contrast, when losses (i.e., payments) were involved, different participants showed quite different patterns of choices. More specifically, although the majority of the participants became increasingly likely to choose to pay later as the delay was increased, some participants appeared to be debt averse, in that they were more likely to choose the immediate payment option when the delay was long than when it was brief. These debt‐averse participants also were more likely to choose to wait for a larger delayed gain than other participants and scored lower on Impulsiveness than those who showed the typical pattern of discounting delayed losses. Taken together, these results suggest that in the case of delayed gains, people differ only quantitatively (i.e., in how steeply they discount), whereas in the case of delayed losses, people differ qualitatively as well as quantitatively, contrary to the common assumption that a single impulsivity trait underlies choices between immediate and delayed outcomes. Copyright © 2016 John Wiley & Sons, Ltd.