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Do favorable beliefs about the self, the future, and one's degree of control over events compromise one's ability to recognize what one cannot accomplish? Previous studies indicating that people with favorable self-beliefs spend more time on unsolvable tasks typically examined persistence with respect to a single unsolvable task or set of tasks. To test whether such seemingly maladaptive persistence would occur in the presence of alternative tasks, we varied whether an initial set of seven unsolvable anagrams was followed by 14 solvable anagrams and examined problem-solving efforts among college students (N = 96) given a 20-min time limit. In the absence of alternatives, most participants worked on the unsolvable trials until the end of the time limit; however, in the presence of alternatives, participants high in optimism or self-mastery beliefs who were not allowed to return to previous trials disengaged from the unsolvable anagrams nearly 4 min sooner than participants low in such beliefs. Additionally, optimists tended to outperform participants low in optimism on the subsequent solvable trials when these trials were said to test an aspect of verbal intelligence different from the initial set. These results suggest that people high in optimism and self-mastery are able to disengage from unsolvable tasks in order to allocate effort to solvable tasks. Implications for the study of nonproductive persistence, the adaptiveness of positive beliefs, and the modification of coping efforts are discussed.