Presupposition triggers, such as the additive particle too, the iterative particle again, and the definite determiner the, are obligatory if their presuppositions are satisfied in the context. This observation is accounted for in the literature by two theories: one based on Maximize Presupposition (e.g., Heim 1991; Percus 2006; Chemla 2008), the other based on Obligatory Implicatures (Bade 2016). In this paper, we report on two experiments in two typologically unrelated languages, Ga (Kwa) and German, which were designed to test the predictions of these two approaches for the insertion of additive particles. The results show that in both languages the insertion of additives is regulated by Obligatory Implicatures, posing challenges for Maximize Presupposition. Following Bade (2016), we assume a division of labor between the two theories in explaining obligatory presupposition effects.