Discourse connectives are words or phrases such as once, since, and on the contrary that explicitly signal the presence of a discourse relation. There are two types of ambiguity that need to be resolved during discourse processing. First, a word can be ambiguous between discourse or non-discourse usage. For example, once can be either a temporal discourse connective or a simply a word meaning “formerly”. Secondly, some connectives are ambiguous in terms of the relation they mark. For example since can serve as either a temporal or causal connective. We demonstrate that syntactic features improve performance in both disambiguation tasks. We report state-of-the-art results for identifying discourse vs. non-discourse usage and human-level performance on sense disambiguation.