Building on Debra Satz's argument that we can design our way out of noxious markets, this essay shifts toward questions of process, paying particular attention to the constraints posed when noxious markets generate supportive political constituencies. Using the case of U.S. housing policy, I make two claims. First, even intentional efforts at using market design to harness the capacities Satz identifies can produce cross-cutting effects, strengthening democracies on some dimensions and weakening them on others. Second, noxious markets can generate supportive constituencies that may undermine reform efforts. Ultimately, a moral housing market requires political supports that can help to broaden communities of fate, build political capacities of those who are persistently underrepresented in local deliberations, and encourage participants to reflect on the consequences of market design.