Traffic classification is still today a challenging prob- lem given the ever evolving nature of the Internet in which new protocols and applications arise at a constant pace. In the past, so called behavioral approaches have been successfully proposed as valid alternatives to traditional DPI based tools to properly classify traffic into few and coarse classes. In this paper we push forward the adoption of behavioral classifiers by engineering a Hierarchical classifier that allows proper classification of traffic into more than twenty fine grained classes. Thorough engineering has been followed which considers both proper feature selection and testing seven different classification algorithms. Results obtained over actual and large data sets show that the proposed Hierarchical classifier outperforms off-the-shelf non hierarchical classification algorithms by exhibiting average accuracy higher than 90%, with precision and recall that are higher than 95% for most popular classes of traffic.