The paper shows that contact-induced grammaticalization is frequently accompanied by frills, that is, by linguistic accretion instead of the commonly expected attrition. This fact adds weight to the important insights gained in recent grammaticalization studies that both language-internal and contact-induced grammaticalization can be analysed in terms of the same set of definitional criteria and that contact-induced grammaticalization always entails language-internal grammaticalization and, hence, the same factors operate in both kinds of change. The explanation proposed here for linguistic accretion in contact-induced grammaticalization capitalizes on the notion of overlap acknowledged in processes of language-internal grammaticalization. In contact-induced grammaticalization, it is shown that overlap is manifested both as a diachronic stage of the grammaticalization development and as a synchronic buffer zone in geographical space.