Statistical systems with high accuracy are very useful in real-world applications. If these systems can capture basic linguistic information, then the usefulness of these statistical systems improve a lot. This paper is an attempt at incorporating linguistic constraints in statistical dependency parsing. We consider a simple linguistic constraint that a verb should not have multiple subjects/objects as its children in the dependency tree. We first describe the importance of this constraint considering Machine Translation systems which use dependency parser output, as an example application. We then show how the current state-ofthe-art dependency parsers violate this constraint. We present two new methods to handle this constraint. We evaluate our methods on the state-of-the-art dependency parsers for Hindi and Czech.