This thesis explores ways to improve the accuracy and coverage of efficient statistical dependency parsing. We employ transition-based parsing with models learned using Support Vector Machines (Cortes and Vapnik, 1995), and our experiments are carried out on French. Transition-based parsing is very fast due to the computational efficiency of its underlying algorithms, which are based on a local optimization of attachment decisions. Our first research thread is thus to increase the syntactic context used. From the arc-eager transition system (Nivre, 2008) we propose a variant that simultaneously considers multiple candidate governors for right-directed attachments. We also test parse correction, inspired by Hall and Novák (2005), which revises each attachment in a parse by considering multiple alternative governors in the local syntactic neighborhood. We find that multiple-candidate approaches slightly improve parsing accuracy overall as well as for prepositional phrase attachment and coordination, two linguistic phenomena that exhibit high syntactic ambiguity. Our second research thread explores semi-supervised approaches for improving parsing accuracy and coverage. We test self-training within the journalistic domain as well as for adaptation to the medical domain, using a two-stage parsing approach based on that of McClosky et al. (2006). We then turn to lexical modeling over a large corpus: we model generalized lexical classes to reduce data sparseness, and prepositional phrase attachment preference to improve disambiguation. We find that semi-supervised approaches can sometimes improve parsing accuracy and coverage, without increasing time complexity.