Binary associations between classifiers are among the most fundamental of UML concepts. However, there is considerable room for disagreement concerning what an association is, semantically; it turns out that at least two different notions are called Associations. This confusion of concepts gives rise to unnecessary complication and ambiguity in the language, which have implications for the modeller because they can result in serious misunderstandings of static structure diagrams; similarly, they have implications for tool developers. In this paper we explore these issues, suggest improvements and clarifications, and demonstrate side-benefits that would accrue.