Covert timing channels are security threats that have concerned the expert community from the beginnings of secure computer networks. In this paper we explore the nature of covert timing channels by studying the behavior of a selection of features used for their detection. Insights are obtained from experimental studies based on ten covert timing channels techniques published in the literature, which include popular and novel approaches. The study digs into the shapes of flows containing covert timing channels from a statistical perspective as well as using supervised and unsupervised machine learning algorithms. Our experiments reveal which features are recommended for building detection methods and draw meaningful representations to understand the problem space. Covert timing channels show high histogramdistance based outlierness, but insufficient to clearly discriminate them from normal traffic. On the other hand, traffic features do show dependencies that allow separating subspaces and facilitate the identification of covert timing channels. The conducted study shows the detection difficulties due to the high shape variability of normal traffic and suggests the implementation of semi-supervised techniques to develop accurate and reliable detectors.