While many school choice studies focus on individual parents' preferences, we simultaneously address the structural context within which families make decisions and the strategies they develop in response. Drawing on in-depth interviews with 24 Black middle-class parents of young children, we demonstrate that they sought well-funded, academically rigorous schools populated by racially diverse middle-class students. Using administrative data, we then show that such schools are exceptionally rare, reflecting the structural realities of US society. To manage the ensuing dilemma, the parents implemented one of two school-selection strategies: 'assiduous rationality', which entailed collecting information to make a maximally informed decision, and 'trusting a close tie', which entailed identifying a network member who had been successful, and following their lead. Regardless of their strategy, the parents exhibited significant institutional mistrust and anxiety. Our results point to the constraint exercised by social structures, which can thwart parental goal realization regardless of class resources.