Previous work on treebank parsing with discontinuous constituents using Linear Context-Free Rewriting systems (LCFRS) has been limited to sentences of up to 30 words, for reasons of computational complexity. There have been some results on binarizing an LCFRS in a manner that minimizes parsing complexity, but the present work shows that parsing long sentences with such an optimally binarized grammar remains infeasible. Instead, we introduce a technique which removes this length restriction, while maintaining a respectable accuracy. The resulting parser has been applied to a discontinuous treebank with favorable results. 1