In this article, I describe the French exceptive construction ne...que. I show that it contains hidden material (specifically, an n-word and the adjective autre 'other') and bring to the fore a paradox, namely the fact that the felicity conditions of the construction seem to vary according to whether this material is realized or remains covert. I argue that the solution to this paradox lies in structural ambiguity, and present the main challenges that a proper analysis of the various semantic components of the construction's meaning has to face.