Counterpossibles are counterfactuals with necessarily false antecedents. The problem of counterpossibles is easiest to state within the nearest possible world framework for counterfactuals: on this approach, a counterfactual is true (roughly) when the consequent is true in the nearest possible world where the antecedent is true. Since counterpossibles have necessarily false antecedents, there is no possible world where the antecedent is true. On the approach favored by Lewis, Stalnaker, Williamson, and others, counterpossibles are all trivially true. I introduce several arguments against the trivial approach. First, it is counter-intuitive to think that all counterpossibles are true. Second, if all counterpossibles were true, then we co...