Presupposition triggers can be divided in two groups on the basis of whether the presuppositions they give rise to are easily defeasible or not. Abusch (2002) calls these two groups “soft” and “hard” triggers. In this paper I argue that the “presuppositions of soft triggers” is a label that actually identifies meaning components that sometimes arise as plain entailments and sometimes as scalar implicatures. I propose a way to derive them based only on alternatives and an independently justified theory of scalar implicatures. This will be able to explain how and when these inferences can be suspended, while also accounting for the “regular” projection behavior when they are not suspended. Furthermore, the proposed system will also account for puzzling cases arising from the interaction between the presupposition of soft triggers and scalar implicatures.