Over the past two decades, the study of moral reasoning has been heavily influenced by Joshua Greene's dual-process model of moral judgment, according to which deontological judgments are typically supported by intuitive, automatic processes while utilitarian judgments are typically supported by reflective, conscious processes. However, most of the evidence gathered in support of this model comes from the study of people's judgments about sacrificial dilemmas, such as Trolley Problems. To which extent does this model generalize to other debates in which deontological and utilitarian judgments conflict, such as the existence of harmless moral violations, the difference between actions and omissions, the extent of our duty to help others, and the good justification for punishment? To find out, we conducted a series of five studies on the role of reflection in these kinds of moral conundrums. In Study 1, participants were asked to answer under cognitive load. In Study 2, participants had to answer under a strict time constraint. In Studies 3 to 5, we sought to promote reflection through exposure to counter-intuitive reasoning problems or direct instruction. Overall, our results offer strong support to the extension of Greene's dual-process model to moral debates on the existence of harmless violations and partial support to its extension to moral debates on the extent of our duty to help others.