This paper studies cross-lingual transfer for dependency parsing, focusing on very low-resource settings where delexicalized transfer is the only fully automatic option. We show how to boost parsing performance by rewriting the source sentences so as to better match the linguistic regularities of the target language. We contrast a data-driven approach with an approach relying on linguistically motivated rules automatically extracted from the World Atlas of Language Structures. Our findings are backed up by experiments involving 40 languages. They show that both approaches greatly outperform the baseline, the knowledge-driven method yielding the best accuracies, with average improvements of +2.9 UAS, and up to +90 UAS (absolute) on some frequent PoS configurations.