Intertemporal choices create a tension between amount maximization, which would favor the larger and later option (LL), and delay minimization, which would promote the smaller and sooner reward (SS). Two common interpretations of intertemporal choice behavior are discussed: looking at LL responses as indicative of self-control, and using intertemporal choices to assess delay aversion. We argue that both interpretations need to take into account motivational confounds, in order to be warranted by data. In intertemporal choices with prepotent, salient stimuli (e.g., food amounts, typically used with nonhuman primates), LL responses could also be indicative of failed inhibition of a "go for more" impulsive response-the opposite of self-control. Similarly, intertemporal choices can be used to measure delay aversion only with respect to the subject's baseline motivation to maximize the reinforcer in question, and this baseline is not always assessed in current experimental protocols. This concern is especially crucial in comparing intertemporal choices across different groups or manipulation. We focus in particular on the effects of reward types on intertemporal choices, presenting two experimental studies where the difference in behavior with monetary versus food rewards is the product of different baseline motivation, rather than variations in delay aversion. We conclude discussing the implications of these and other similar recent findings, which are far-reaching.