Abstract: (...or, counterfactual invariance deciders and the analysis of necessity.) In my PhD thesis I gave an account of the conditions under which a proposition is necessarily true (in the sense isolated by Kripke). The account crucially involved a property of propositions called 'inherent counterfactual invariance'. The proposition 'Air is airy' (discussed recently by Jens Kipper) shows this account to be false. In this talk I will explain this, before suggesting that we try for an analysis which appeals to a relation of counterfactual invariance deciding between (sets of) propositions. This relation is plausibly a priori tractable, and can naturally (if more contentiously) be thought of as broadly semantic.