This article defends Noël Carroll’s incongruity theory of humour from the pressing criticism that his articulation of incongruity is too vague to serve as a key notion of the theory. I first distinguish between two versions of the criticism of vagueness: the claim that Carroll’s notion of incongruity is vacuous, and the claim that it allows for shoehorning. To reject the first claim, I put Carroll’s notion of incongruity to the test by analysing complex comic texts, demonstrating that it is not vacuous as it allows for capturing their similarities and differences. In response to the second claim, I claim that Carroll’s notion of incongruity should be amended adding a pertinence condition, which requires that the elements establishing the incongruity are part of the same context. Finally, I show that the pertinence condition helps Carroll, replying to a set of counterexamples moved to his sufficiency conditions too.