Children often say that possible events are impossible, and only gradually come to see these events as possible. For instance, they often deny that people could do unusual things, like own a pet peacock, or immoral things, like stealing or lying. These possibility denials are surprising. For instance, children have first-hand experience with the very moral violations they say are impossible. In two experiments (total N = 220), we provide evidence that children's possibility denials can nonetheless be taken at face value and do not merely arise from quirks in how children understand questions about possibility. We do this by showing that these denials also arise in children's judgments of actuality--their judgments about what has actually happened and about which assertions of actual events could be true. In Experiment 1, children aged 4-7 judged whether ordinary, immoral, and improbable events could happen or had ever happened. With both judgments, children mostly responded affirmatively to ordinary events, often responded negatively for immoral events, and mostly responded negatively to improbable ones. In Experiment 2, children aged 5-7 judged if assertions of the three kinds of events could be true, and the same pattern emerged again. Together, these findings show that children's denials of immoral and conceptually improbable events extend beyond their judgments about what is possible and match their inferences about what is actual. These correspondences across judgments suggest that children drew on a single procedure, or set of procedures, for assessing possibility.