The idea motivating their account, Cappelen and Lepore (C&L) say in Insensitive Semantics (2005), is that semantic content is context invariant, and that all colleagues who take, or even consider, different accounts are just on the wrong track. It is the purpose of their book to disprove all alternative accounts by way of an argument ‘by elimination’. The conclusion they arrive at is that their own account must be accepted by everyone as “the only game in town at the end of the day”. The present paper is intended to examine this conclusion; its more significant findings are these. Firstly, C&L’s account is not, as they suggest, strictly minimalist, but in fact just a moderate version of contextualism. Secondly, prematurely associating semantical incompleteness and context sensitivity, they overlook some possible alternatives to their own view, among them at least one that is attractive. Thirdly, their argument ‘by elimination’ has an inductive structure, but is inexhaustive, and therefore inconclusive. Fourthly, for several different reasons, their attempts to reject arguments in favour of semantical incompleteness do not work. Finally, their contention that arguments in favour of semantical incompleteness employ metaphysical premisses for semantical conclusions rests on a faulty interpretation of these arguments. In the light of these findings, it is concluded that the central argument of Insensitive Semantics fails.