Despite its somewhat marginal occurrence, unattainability has been acknowledged as a genuine problematic element for the semantic analysis of modal constructions, particularly for those expressing desires (Heim in J Semant 9(3):183–221, 1992; Portner in Nat Lang Semant 5(2):167–211, 1997). However, considerably less attention has been given to unattainable duties. In this article, I suggest that just as worlds that are deemed desirable are not necessarily linked to worlds considered candidates for actuality, some circumstantial arrangements allow for obligational expressions the semantics of which evoke worlds that are deemed obligatory yet unattainable. As I will show, a careful examination of unattainable duties constructions reveals some unexplored semantic aspects of obligational ascriptions that are particularly relevant for the development of both X-marking and modal-tense interaction theories. This article provides a philosophical and linguistic account of the meaning and use of such constructions.