This paper proposes an extension of Dependency Tree Semantics (DTS), an underspecified logic originally proposed in [20], that uniformily implements constraints on Nested Quantification, Island Constraints and logical Redundancy. Unfortunately, this extension makes the complexity exponential in the number of NPs, in the worst cases. Nevertheless, we conducted an experiment on the Turin University Treebank [6], a Treebank of italian sentences annotated in a syntactic dependency format, whose results seem to indicate that these cases are very rare in real sentences.