During the last decade, the Computational Linguistics community has shown an increased interest in Dependency Treebanks. Several groups have developed new annotated corpora using dependency representation, while other people have proposed several automatic conversion algorithms to transform available Phrase Structure (PS) treebanks into Dependency Structure (DS) notation. Such projects typically refer to Tesnière as the father of dependency syntax, but little attempt has been made to explain how the chosen representation relates to the original work. A careful comparison reveals substantial differences: modern DS annotations discard some relevant features characterizing Tesnière’s model. This paper is presenting our attempt to go back to the roots of dependency theory, and show how it is possible to transform a PS English treebank to a DS notation that is closer to the one proposed by Tesnière, which we will refer to as TDS. We will show how this representation can incorporate all main advantages of modern DS, while avoiding well known problems concerning the choice of heads, and better representing common linguistic phenomena such as coordination.