What is the minimal set of fragments that achieves maximal parse accuracy?

We aim at finding the minimal set of fragments which achieves maximal parse accuracy in Data Oriented Parsing. Experiments with the Penn Wall Street Journal treebank show that counts of almost arbitrary fragments within parse trees are important, leading to improved parse accuracy over previous models tested on this treebank (a precision of 90.8% and a recall of 90.6%). We isolate some dependency relations which previous models neglect but which contribute to higher parse accuracy.