Linguistic phenomena (e.g., words and syntactic structure) co-occur with a wide variety of meanings. These systematic correlations can help readers to interpret a text and create predictions about upcoming material. However, to what extent these correlations influence discourse processing is still unknown. We address this question by examining whether clause type serves as a cue for discourse relations. We found that the co-occurrence of gerund-free adjuncts and specific discourse relations found in natural language is also reflected in readers' offline expectations for discourse relations. However, we also found that clause structure did not facilitate the online processing of these discourse relations, nor that readers have a preference for these relations in a paraphrase selection task. The present research extends previous research on discourse relation processing, which mostly focused on lexical cues, by examining the role of non-semantic cues. We show that readers are aware of correlations between clause structure and discourse relations in natural language, but that, unlike what has been found for lexical cues, this information does not seem to influence online processing and discourse interpretation.