Factorization is the operation of transforming a production in a Linear Context-Free Rewriting System (LCFRS) into two simpler productions by factoring out a subset of the nonterminals on the production’s righthand side. Factorization lowers the rank of a production but may increase its fan-out. We show how to apply factorization in order to minimize the parsing complexity of the resulting grammar, and study the relationship between rank, fanout, and parsing complexity. We show that it is always possible to obtain optimum parsing complexity with rank two. However, among transformed grammars of rank two, minimum parsing complexity is not always possible with minimum fan-out. Applying our factorization algorithm to LCFRS rules extracted from dependency treebanks allows us to find the most efficient parsing strategy for the syntactic phenomena found in non-projective trees. 1