The reverse-reward contingency task presents 2 food sets to an animal, and they are required to choose the smaller of the 2 sets in order to receive the larger food set. Intriguingly, the majority of species tested on the reverse-reward task fail to learn this contingency in the absence of large trial counts, correction trials, and punishment techniques. The unique difficulty of this seemingly simple task likely reflects a failure of inhibitory control which is required to point toward a smaller and less desirable reward rather than a larger and more desirable reward. This failure by chimpanzees and other primates to pass the reverse-reward task is striking given the self-control they exhibit in a variety of other paradigms. For example, chimpanzees have consistently demonstrated a high capacity for delay of gratification in order to maximize accumulating food rewards in which foods are added item-by-item to a growing set until the subject consumes the rewards. To study the mechanisms underlying success in the accumulation task and failure in the reverse-reward task, we presented chimpanzees with several combinations of these 2 tasks to determine when chimpanzees might succeed in pointing to smaller food sets over larger food sets and how the nature of the task might determine the animals’ success or failure. Across experiments, 3 chimpanzees repeatedly failed to solve the reverse-reward task, whereas they accumulated nearly all food items across all instances of the accumulation self-control task, even when they had to point to small amounts of food to accumulate larger amounts. These data indicate that constraints of these 2 related but still different tasks of behavioral inhibition are dependent upon the animals’ perceptions of the choice set, their sense of control over the contents of choice sets, and the nature of the task constraints.