Abstract: In moral and political philosophy, some people emphasize the importance of searching for “reflective equilibrium,” in which (broadly speaking) general principles align with convictions about particular cases, and vice-versa. There is a close analogue in constitutional law; the search for reflective equilibrium plays a central role. Some theories of constitutional interpretation seem to call for results that are inconsistent with “fixed points” in constitutional law (where “fixed points” are understood as particular holdings, such as Brown v. Board of Education, to which people have exceedingly strong commitments). The risk to fixed points strongly counts against such theories. The reason is that among the reasonable candidates, any theory of interpretation must be defended on the ground that it would make our constitutional order better rather than worse. It follows that if a theory would lead to rejection to fixed points, it has a clear strike against it. Many participants in debates about constitutional theory implicitly agree on this point, and they had better; there is no way to choose a theory of constitutional interpretation that refuses to seek reflective equilibrium, which means that consideration of fixed points is essential.