Timothy Williamson has defended two hypotheses concerning counterfactual conditionals: that necessity can be defined in counterfactual terms; and that we follow a heuristic to the effect that a counterfactual is assessed by assessing the consequent while counterfactually supposing the antecedent. The two hypotheses form the bedrock for a program aiming to reduce the epistemology of modality to the epistemology of counterfactual thinking. This paper argues that the pair of theses, if construed as Williamson intends it, has the unwanted consequence of trivializing our judgements about necessity and possibility, thus threatening the reductionist program. Trivialization can be avoided if we suitably weaken a background hypothesis concerning the way we assess pairs of mutually inconsistent statements. One important corollary of the proposed solution is that the suppositional heuristic need not yield incorrect judgements about counterpossibles, pace Williamson. Moreover, the proposal remains compatible with vacuism, the view that all counterpossibles are true.