Presuppositions are traditionally understood as a set of backgrounded, and thus not-at-issue, projective inferences that are taken for granted by communicators. In the last decades it has been observed that presuppositions behave heterogeneously, which lead to a discussion about the distinction between soft and hard presupposition triggers. In this paper, another property of presuppositions is exploited to test if there is evidence for a soft-hard dichotomy: their reluctance to answer the current Question Under Discussion, as observed by Simons et al. (2010). Using a modified acceptability judgment task, we tested children between 4 and 6 years of age and adult controls. Audio recordings with image stills featured both kinds of presupposition triggers in at-issue and non-at-issue exchanges, with non-restrictive relative clauses as controls, as they are conventionally not-at-issue but usually add new information. The results indicate that, for our adult participants, such backgroundedness violations are worse in the case of hard triggers, whereas soft triggers are markedly less deviant in such cases. Children are also sensitive to the soft-hard distinction but react less strongly than adult counterparts to oddity effects. Additionally, hard triggers pattern with non-restrictive relative clauses in both groups.