Recent work identifies two properties that appear particularly relevant to the characterization of graph-based dependency models of syntactic structure: the absence of interleaving substructures (well-nestedness) and a bound on a type of discontinuity (gap-degree ≤ 1) successfully describe more than 99% of the structures in two dependency treebanks (Kuhlmann and Nivre 2006). Bodirsky et al. (2005) establish that every dependency structure with these two properties can be recast as a lexicalized Tree Adjoining Grammar (LTAG) derivation and vice versa. However, multi-component extensions of TAG (MC-TAG), argued to be necessary on linguistic grounds, induce dependency structures that do not conform to these two properties (Kuhlmann and Möhl 2006). In this paper, we observe that several types of MC-TAG as used for linguistic analysis are more restrictive than the formal system is in principle. In particular, tree-local MC-TAG, tree-local MC-TAG with flexible composition (Kallmeyer and Joshi 2003), and special cases of set-local TAG as used to describe certain linguistic phenomena satisfy the well-nested and gap degree ≤ 1 criteria. We also observe that gap degree can distinguish between prohibited and allowed wh-extractions in English, and report some preliminary work comparing the predictions of the graph approach and the MC-TAG approach to scrambling.