In this paper, we try to see how insights from morphology and grammaticalisation can be combined. Two approaches to the semantics of inflectional affixes are contrasted. According to one, affixes have no meaning, according to another, affixes have meaning just like lexical items. Given insights from grammaticalisation, a middle way, associated with the No Blur Principle, seems more appealing than either of these extremes. The No Blur Principle is illustrated, and its predictions are shown to be tenable, also in apparent counterexamples from Scandinavian inflection classes. Inflection classes are sometimes assigned on "strange" bases. This is because there are "local" generalisations in inflection class assignment (as in gender, where such generalisations have been called "crazy"). Our view of grammaticalisation also supports the idea of a language as a "system" of low-level regularities, even if this picture seems unusual. (Contains 4 tables.)