This paper explores the relation between the interpretations of while in English and mentre in Italian introducing adverbial clauses. Central while/mentre clauses express a temporal/aspectual modification of the proposition in the host clause. Peripheral while/mentre clauses make accessible a proposition from the discourse context enhancing the relevance of the host proposition. In one approach, clauses introduced by adversative while/mentre are analyzed as ‘less integrated’ with the associated clause than those introduced by temporal while/mentre. In another approach, adverbial clauses introduced by adversative while/mentre are considered not syntactically integrated with the host clause. This paper re-examines the nature of the syntactic integration of the adverbial clauses with the host clause, revealing a parallelism between the adversative peripheral while/mentre clauses and speaker-related sentential adverbs, leading to the conclusion that the non-integration analysis is not appropriate for this type of peripheral clauses and that any analysis must be aligned with that of the relevant non-clausal adverbials, supporting Frey (2018, 2020a, b). We also argue that central adverbial clauses recycled as speech event modifiers must be considered non-integrated. Concretely, we propose that they are integrated in discourse, through a specialized layer FrameP (Haegeman & Greco 2018).