Syntactic parsing requires a fine balance between expressivity and complexity, so that naturally occurring structures can be accurately parsed without compromising efficiency. In dependency-based parsing, several constraints have been proposed that restrict the class of permissible structures, such as projectivity, planarity, multi-planarity, well-nestedness, gap degree, and edge degree. While projectivity is generally taken to be too restrictive for natural language syntax, it is not clear which of the other proposals strikes the best balance between expressivity and complexity. In this paper, we review and compare the different constraints theoretically, and provide an experimental evaluation using data from two treebanks, investigating how large a proportion of the structures found in the treebanks are permitted under different constraints. The results indicate that a combination of the well-nestedness constraint and a parametric constraint on discontinuity gives a very good fit with the linguistic data.