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-to-the-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. We integrate the various pointwise decisions as latent variables in a single arc-level SVM classifier. This novel framework allows us to combine nine pointwise filters, and adjust their sensitivity using a shared threshold based on arc length. Our system filters 32% more arcs than the independently-trained classifiers, without reducing filtering speed. This leads to faster parsing with no reduction in accuracy.