A growing body of school choice research has shown that when school choice policies are not designed to racially or socioeconomically integrate schools, that is, are "colorblind" policies, they generally manage to do the opposite, leading to greater stratification and separation of students by race and ethnicity across schools and programs. Since white, advantaged parents are more likely to get their children into the highest-status schools regardless of the school choice policy in place, we believed that more research was needed on how those parents interact with school choice policies and whether they would support changes to those policies that would lead to less segregation across schools. Our interviews with advantaged New York City parents suggest that many are bothered by the segregation but that they are concerned that their children gain access to the "best" (mostly white) schools. The contradictions inherent in their choices are reconcilable, we argue, by offering more diverse and undivided school options. (Contains 3 tables and 1 note.)