We propose a dependency parsing pipeline, in which the parsing of long-distance projections and localized dependencies are explicitly decomposed at the input level. A chosen baseline dependency parsing model performs only on ‘carved’ sequences at the second stage, which are transformed from coarse constituent parsing outputs at the first stage. When k-best constituent parsing outputs are kept, a third-stage is required to search for an optimal combination of the overlapped dependency subtrees. In this sense, our dependency model is subtree-factored. We explore alternative approaches for scoring subtrees, including feature-based models as well as continuous representations. The search for optimal subset to combine is formulated as an ILP problem. This framework especially benefits the models poor on long sentences, generally improving baselines by 0.75-1.28 (UAS) on English, achieving comparable performance with high-order models but faster. For Chinese, the most notable increase is as high as 3.63 (UAS) when the proposed framework is applied to first-order parsing models.