It is commonly assumed that teasing is restricted to encounters among intimates or close acquaintances. As a result of examining initial interactions among (American and Australian) speakers of English, however, this article shows that teasing also occurs between persons who are becoming acquainted. Analysis reveals that tease sequences unfold across three actions that constitute the tease as an invitation to intimacy: a teasable action on the part of the target, the tease proper and a moment of interactionally generated affiliation. Given teasing is one way of criticising another, it constitutes a potential breach of tact or interactional propriety. In initial interactions, however, participants can construe this potential impropriety as an invitation to intimacy, as it involves the proposal of a shared ironic stance that may be either accepted or declined by the target of the tease.