The focus of this article is the developments in contemporary Danish of direct vis-à-vis indirect borrowing strategies regarding English expressions. In order to distinguish direct borrowings of such items from codeswitches, the author presents a number of approaches found in the existing literature and suggests an operational definition of codeswitching. Eight scenarios involving the adoption and/or translation of English multi-word or polymorphemic expressions are presented, and the trajectories over three decades of forty-four Danish Anglicisms representing all scenarios are investigated. The basis for this empirical research is the gigantic Danish text archive Infomedia, and the results show the relative success of ‘invisible’ multi-word and polymorphemic expressions: Anglicisms using all-Danish material but calquing their English etymons and thus representing Anglo-American concepts in Danish disguise.