Past work has demonstrated that people’s moral judgments can influence their judgments in a number of domains that might seem to involve straightforward matters of fact, including judgments about freedom, causation, the doing/allowing distinction, and intentional action. The present studies explore whether the effect of morality in these four domains can be explained by changes in the relevance of alternative possibilities. More precisely, we propose that moral judgment influences the degree to which people regard certain alternative possibilities as relevant, which in turn impacts intuitions about freedom, causation, doing/allowing, and intentional action. Employing the stimuli used in previous research, Studies 1a, 2a, 3a, and 4a show that the relevance of alternatives is influenced by moral judgments and mediates the impact of morality on non-moral judgments. Studies 1b, 2b, 3b, and 4b then provide direct empirical evidence for the link between the relevance of alternatives and judgments in these four domains by manipulating (rather than measuring) the relevance of alternative possibilities. Lastly, Study 5 demonstrates that the critical mechanism is not whether alternative possibilities are considered, but whether they are regarded as relevant. These studies support a unified framework for understanding the impact of morality across these very different kinds of judgments.