Typical approaches to study self-control present subjects with a simultaneous choice between a larger-later (LL) reinforcer and a smaller-sooner (SS) reinforcer. In contrast, in patch-leaving tasks, subjects choose between staying at a patch for an SS (or LL) reinforcer and leaving for an LL (or SS) reinforcer. Previous studies show that blue jays, monkeys, humans, and rats prefer the SS reinforcer in binary-choice tasks, whereas the same subjects prefer the LL reinforcer in equivalent patch-leaving tasks. The current study systematically replicated this research using pigeons. Six pigeons responded in a binary-choice task and in two patch-leaving tasks in which staying led to an LL (Patch-L) or SS (Patch-S) reinforcer. Across conditions, the SS reinforcer delay varied from 5 to 55 s; the LL reinforcer delay was always 60 s. In binary-choice conditions, subjects preferred the SS reinforcer. In Patch-L and Patch-S conditions, subjects preferred the LL and SS reinforcer, respectively, reflecting a bias to stay at the patch. This bias persisted when the stay response was more effortful and when the delays to both reinforcers were equal. This may reflect a species-specific win-stay bias and the differential consequences of staying (which led to a stimulus signaling food) versus leaving (which led to a stimulus never associated with food). Thus, we propose a conditioned-reinforcement account of intertemporal choice in patch-leaving contexts. We suggest several avenues for further investigations of the mechanisms underlying intertemporal choice in different contexts and question the economic equivalence of the operant and patch-leaving procedures. (PsycInfo Database Record (c) 2024 APA, all rights reserved).