This chapter explores how morality can be rational if moral intuitions are resistant to rational reflection. There are two parts to this question. The normative problem is whether there is a model of moral justification which can show that morality is a rational enterprise given the facts of moral dumbfounding. Appealing to the model of reflective equilibrium for the rational justification of moral intuitions solves this problem. Reflective equilibrium views the rational justification of morality as a back-and-forth balancing between moral theory and moral intuition, and therefore does not require that individual moral intuitions be directly responsive to rational reflection. The psychological problem is whether human psychology actually implements the processes required for reflective equilibrium. The psychological problem is far more difficult, and requires appealing to a dual-process view of moral judgement that regards moral intuitions and moral theories as belonging to different mental systems.