In this paper, we focus on parsing rare and non-trivial constructions, in particular ellipsis. We report on several experiments in enrichment of training data for this specific construction, evaluated on five languages: Czech, English, Finnish, Russian and Slovak. These data enrichment methods draw upon self-training and tri-training, combined with a stratified sampling method mimicking the structural complexity of the original treebank. In addition, using these same methods, we also demonstrate small improvements over the CoNLL-17 parsing shared task winning system for four of the five languages, not only restricted to the elliptical constructions.