The precise formulation of derivation for treeadjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that the definition of tree-adjoining derivation must be reformulated in order to manifest the proper linguistic dependencies in derivations. The particular proposal is both precisely characterizable, through a compilation to linear indexed grammars, and computationally operational, by virtue of an efficient algorithm for recognition and parsing. .