Tree-Adjoining Grammars (TAG) have been used both for syntactic parsing, with sentential grammars, and for discourse parsing, with discourse grammars. But the modeling of discourse connectives (coordinate conjunctions, subordinate conjunctions , adverbs.. .) in TAG-based formalisms for discourse differ from their modeling in sentential grammars. Because of this mismatch, an intermediate, not TAG-related, processing step is required between the sentential and the discourse processes, both in parsing and in generation. We present a method to smoothly interface sentential and discourse TAG grammars, without using such an intermediate processing step. This method is based on Abstract Categorial Grammars (ACG) and relies on the modularity of the latter. It also provides the possibility, as in D-STAG, to build discourse structures that are direct acyclic graphs (DAG) and not only trees. All the examples may be run and tested with the appropriate software.