If a speaker utters a sentence p containing a presupposition trigger that activates a presupposition q, and q does not belong to the common ground of presuppositions, it is a case of presupposition failure. If this occurs, speakers are required to repair the failure to make sense of the utterance. According to Glanzberg, two subcategories of being infelicitous may emerge in the case of presupposition failure: one is that strong presuppositions lead to obligatory repair, and the other is that weak presuppositions lead only to an optional repair. Following Glanzberg's suggestion, in this paper we present the results of an experiment supporting the idea that, depending on the kind of trigger, processing the information conveyed by a presupposition can be either optional or mandatory in case of presupposition failure. The conclusion of this paper is that the cognitive demands of different presupposition triggers do not primarily depend on whether they optionally or obligatorily lead to process the presuppositions activated. Rather, their cognitive demands seem to be related with the complexity of the mental representation of the presupposition required.