Valency of lexical units (i.e. the sets of their obligatory and optional dependents) constitutes the main link between lexicon and grammar. As handled up to now by J. Panevova and others in the Functional Generative Description, valency provides a very good starting point for the testing of this approach in the Prague Dependency Treebank. The morphemic and especially syntactic annotation of large segments of free texts confirm that this description has essentially been formulated adequately. Even so, certain issues of valency deserve further discussion. This article partly summarizes earlier research in the Charles University Theoretical and Computational Linguistics group and adds new results. It aims to document how issues concerning a hierarchy of the types of dependency relations, the orientation of these relations, the usefulness of recognizing a third class of dependents 'between' arguments and adjuncts, etc., can be handled in useful ways using this background.