Abstract It is a familiar point that we can use generic sentences to express generalisations that are tolerant to exceptions and then go on to state those exceptions explicitly. It is a less familiar point that switching the order of the generics has deleterious effects on their felicity. For example, the sequences ‘Ravens are black, but albino ravens aren’t’ is perfectly felicitous and judged to be true, whereas its reverse ‘Albino ravens aren’t black, but ravens are’ is infelicitous and contradictory-sounding. This paper argues that such sequences pose a problem for extant theories of generics: while they have no trouble predicting the felicity of the first sequence of generics, they are unable to explain why reversing the order results in infelicity. I propose to account for these observations by adopting a dynamic semantic theory of generic sentences.