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Accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists, because couples view pairs of jobs as complements. A stable matching may not exist when couples are present. This paper's main result is that a stable matching exists when there are relatively few couples and preference lists are sufficiently short relative to market size. We also discuss incentives in markets with couples. We relate these theoretical results to the job market for psychologists, in which stable matchings exist for all years of the data, despite the presence of couples.