Understanding the syntactic structure of a sentence is a necessary preliminary to understanding its semantics and therefore for many practical applications. The field of natural language processing has achieved a high degree of accuracy in parsing, at least in English. However, the syntactic structures produced by the most commonly used parsers are less detailed than those structures found in the treebanks the parsers were trained on. In particular, these parsers typically lack the null elements used to indicate wh-movement, control, and other phenomena. This thesis presents a system for inserting these null elements into parse trees in English. It then examines the problem in Arabic, which motivates a second, joint- inference system which has improved performance on English as well. Finally, it examines the application of information derived from the Google Web 1T corpus as a way of reducing certain data sparsity issues related to wh-movement.