Explaining why the same passage may have different rhetorical structures when conveyed in different languages remains an open question. Starting from a trilingual translation corpus, this paper aims to provide a new qualitative method for the comparison of rhetorical structures in different languages and to specify why translated texts may differ in their rhetorical structures. To achieve these aims we have carried out a contrastive analysis, comparing a corpus of parallel English, Spanish and Basque texts, using Rhetorical Structure Theory. We propose a method to describe the main linguistic differences among the rhetorical structures of the three languages in the two annotation stages (segmentation and rhetorical analysis). We show a new type of comparison that has important advantages with regard to the quantitative method usually employed: it provides an accurate measurement of inter-annotator agreement, and it pinpoints sources of disagreement among annotators. With the use of this new method, we show how translation strategies affect discourse structure.