In a proposal, Vijay-Shanker and Joshi presented a definition for combining the two formalisms Tree Adjoining Grammars and PATR unification. The essential idea for that combination is the separation of the two recursion operations - adjoining and unification - to preserve all properties of both formalisms which is not desirable for natural language applications. In this paper, a definition for the integrated use of both processes is given and the remaining properties of the resulting formalism are discussed - especially weighing the appropriateness of this definition for natural language processing.