Prepositions and conjunctions are two of the largest remaining bottlenecks in parsing. Across various existing parsers, these two categories have the lowest accuracies, and mistakes made have consequences for downstream applications. Prepositions and conjunctions are often assumed to depend on lexical dependencies for correct resolution. As lexical statistics based on the training set only are sparse, unlabeled data can help ameliorate this sparsity problem. By including unlabeled data features into a factorization of the problem which matches the representation of prepositions and conjunctions, we achieve a new state-of-the-art for English dependencies with 93.55% correct attachments on the current standard. Furthermore, conjunctions are attached with an accuracy of 90.8%, and prepositions with an accuracy of 87.4%.