NPs in English and German adhere to a specific structural requirement: a pre-modifier of a noun may not have a post-modifier. A Dependency Grammar analysis of the phenomenon is provided. The analysis is summarized in terms of a structural constraint called the Left Elbow Constraint. This constraint states that a pre-dependent of a noun may not have a post-dependent. The prohibited structure forms a left elbow underneath the noun. The constraint is valid in a uniform manner for English and German, and it explains some curious word order differences in NPs across the two languages.