The present article focuses on the pragmaticalisation of the French temporal phrase "à un moment donné" (“at one point”, “at a given moment”), and more particularly on one question (that was left unresolved by a previous study) about the role of the adjective "donné" (“given”). We hypothesize that it plays in favor of a greater subjective implication (favouring thus the pragmaticalisation of the phrase). We verify this hypothesis by a systematic examination of "à un moment" vs "à un moment donné", based on the oral part of the Corpus Study for Contemporary French. We also consider other possible variants: variants with "il y a" ("there is”) ("il y a un moment (donné)" / “there is a given moment”) or without the preposition "à" (“at”) ("un moment (donné)" / “a given moment”).