Graph-based dependency parsing can be sped up significantly if implausible arcs are eliminated from the search-space before parsing begins. State-of-the-art methods for arc filtering use separate classifiers to make pointwise decisions about the tree; they label tokens with roles such as root, leaf, or attaches-tothe-left, and then filter arcs accordingly. Because these classifiers overlap substantially in their filtering consequences, we propose to train them jointly, so that each classifier can focus on the gaps of the others. .