Discourse markers and their functions have been modeled through a large number of very diverse frameworks. Most of these models target written language and the discourse relations that hold between sentences. In this paper, we present, assess and apply a new annotation taxonomy that targets discourse markers (instead of discourse relations) in spoken language and addresses their polyfunctionality in an alternative way. In particular, its main innovative feature is to distinguish between two independent layers of semantic-pragmatic information (i.e., domains and functions) which, once combined, provide a fine-grained disambiguation of discourse markers. We compare the affordances of this model to existing proposals, and illustrate them with a corpus study. A sample of conversational French containing 423 discourse marker tokens was fully analyzed by two independent annotators. We report on inter-annotator agreement scores, as well as quantitative analyses of the distribution of domains and functions in the sample. Both powerful and economical, this proposal advocates a flexible and modular approach to discourse analysis, and paves the way for further corpus-based studies on the challenging category of discourse markers.