Prior use of machine learning in genre classification used a list of labels as classification categories. However, genre classes are often organised into hierarchies, e.g., covering the subgenres of fiction. In this paper we present a method of using the hierarchy of labels to improve the classification accuracy. As a testbed for this approach we use the Brown Corpus as well as a range of other corpora, including the BNC, HGC and Syracuse. The results are not encouraging: apart from the Brown corpus, the improvements of our structural classifier over the flat one are not statistically significant. We discuss the relation between structural learning performance and the visual and distributional balance of the label hierarchy, suggesting that only balanced hierarchies might profit from structural learning.