Two apparently opposing DOP models exist in the literature: one which computes the parse tree involving the most frequent subtrees from a treebank and one which computes the parse tree involving the fewest subtrees from a treebank. This paper proposes an integration of the two models which outperforms each of them separately. Together with a PCFGreduction of DOP we obtain improved accuracy and efficiency on the Wall Street Journal treebank. Our results show an 11% relative reduction in error rate over previous models, and an average processing time of 3.6 seconds per WSJ sentence.