In this paper we present a multidimensional approach to utterance segmentation and automatic dialogue act classification. We show that the use of multiple dimensions in distinguishing and annotating units not only supports a more accurate analysis of human communication, but can also help to solve some notorious problems concerning the segmentation of dialogue into functional units. We introduce the use of per-dimension segmentation for dialogue act taxonomies that feature multi-functionality and show that better classification results are obtained when using a separate segmentation for each dimension than when using one segmentation that fits all dimensions. Three machine learning techniques are applied and compared on the task of automatic classification of multiple communicative functions of utterances. The results are encouraging and indicate that communicative functions in important dimensions are easy machine-learnable.