Exploiting data from a parallel treebank recently developed for Italian, English and French, the paper discusses issues related to the development of a dependency-based alignment system. We focus on the alignment of linguistic expressions and constructions which are structurally different in the languages that have to be aligned, and on how to deal with them using dependency rather than constituency. In order to analyze in particular the shifts related to syntactic structure, we present a selection of cases where a dependency-based and a constituency-based representation has been applied and compared.