To explain trade-offs in choice, researchers have proposed myriad phenomena and decision rules, each paired with separate theories and idiosyncratic vocabularies. Yet most choice problems are ultimately resolved with one of just two types of solutions: mixed or extreme. For example, people adopt mixed solutions for resolving trade-offs when they allow exercising to license indulgence afterward (balancing between goals), read different literary genres (variety seeking), and order medium-sized coffees (the compromise effect). By contrast, when people adopt extreme solutions for resolving these exact same trade-offs, they exhibit highlighting, consistency seeking, and compromise avoidance, respectively. Our review of the choice literature first illustrates how many seemingly unrelated phenomena actually share the same underlying psychology. We then identify variables that promote one solution versus the other. These variables, in turn, systematically influence which of opposite choice effects arise (e.g., highlighting versus balancing). Finally, we demonstrate how several mistakes people purport to make can potentially instead be reinterpreted as mixed solutions for resolving trade-offs. We conclude with guidance for distinguishing mistakes from mixed solutions.