In this paper, we analyze the impact of various dependency representations for various constructions on the general parsing accuracy and on the parsing accuracy of these constructions. We focus on the analysis of coordination constructions, complex predicates, and punctuation mark attachment. We use Latvian Treebank as a dataset, thus, providing insight for an inflective language with a rather free word order. Experiments with MaltParser, a transition-based parser, show clear difference in learnability of various representations for the considered constructions. Future work would include carrying out comparable experiments with a graph-based dependency parser like MSTParser.