Human annotation of discourse corpora typically results in segmentation hierarchies that vary in their degree of agreement. This paper presents several techniques for unifying multiple discourse annotations into a single hierarchy, deemed a "gold standard" - the segmentation that best captures the underlying linguistic structure of the discourse. It proposes and analyzes methods that consider the level of embeddedness of a segmentation as well as methods that do not. A corpus containing annotated hierarchical discourses, the Boston Directions Corpus, was used to evaluate the "goodness" of each technique, by comparing the similarity of the segmentation it derives to the original annotations in the corpus. Several metrics of similarity between hierarchical segmentations are computed: precision/recall of matching utterances, pairwise inter-reliability scores (κ), and non-crossing-brackets. A novel method for unification that minimizes conflicts among annotators outperforms methods that require consensus among a majority for the κ and precision metrics, while capturing much of the structure of the discourse. When high recall is preferred, methods requiring a majority are preferable to those that demand full consensus among annotators.