Young children tend to deny the possibility of events that violate their expectations, including events that are merely improbable, like making onion-flavored ice cream or owning a crocodile as a pet. Could this tendency be countered by teaching children more valid strategies for judging possibility? We explored this question by training children aged 4-12 (n = 128) to consider either the similarity between the target event and unusual events that have actually occurred or causal mechanisms that might bring the target event about. Both trainings increased children's acceptance of improbable events but only for the types of events addressed during training. Older children were more likely to accept improbable events, as were children who scored higher on a measure of cognitive reflection, but neither age nor cognitive reflection moderated the effects of training. These findings indicate that children can use both similarity and causality to assess possibility, but the use of this information is highly circumscribed, further demonstrating how robustly children conflate improbability with impossibility.