Stanford Dependencies (SD) represent nowadays a de facto standard as far as dependency annotation is concerned. The goal of this paper is to explore pros and cons of different strategies for generating SD annotated Italian texts to enrich the existing Italian Stanford Dependency Treebank (ISDT). This is done by comparing the performance of a statistical parser (DeSR) trained on a simpler resource (the augmented version of the Merged Italian Dependency Treebank or MIDT+) and whose output was automatically converted to SD, with the results of the parser directly trained on ISDT. Experiments carried out to test reliability and effectiveness of the two strategies show that the performance of a parser trained on the reduced dependencies repertoire, whose output can be easily converted to SD, is slightly higher than the performance of a parser directly trained on ISDT. A non-negligible advantage of the first strategy for generating SD annotated texts is that semi-automatic extensions of the training resource are more easily and consistently carried out with respect to a reduced dependency tag set. Preliminary experiments carried out for generating the collapsed and propagated SD representation are also reported.