We propose a new variant of Tree-Adjoining Grammar that allows adjunction of full wrapping trees but still bears only context-free expressivity. We provide a transformation to context-free form, and a further reduction in probabilistic model size through factorization and pooling of parameters. This collapsed context-free form is used to implement efficient grammar estimation and parsing algorithms. We perform parsing experiments the Penn Treebank and draw comparisons to Tree-Substitution Grammars and between different variations in probabilistic model design. Examination of the most probable derivations reveals examples of the linguistically relevant structure that our variant makes possible. 1