In this work we present our approach to model selection for statistical parsing via boosting. The method is used to target the inefficiency of current feature selection methods, in that it allows a constant feature selection time at each iteration rather than the increasing selection time of current standard forward wrapper methods. With the aim of performing feature selection on very high dimensional data, in particular for parsing morphologically rich languages, we test the approach, which uses the multiclass AdaBoost algorithm SAMME (Zhu et al., 2006), on French data from the French Treebank, using a multilingual discriminative constituency parser (Crabbe, 2014). Current results show that the method is indeed far more efficient than a naive method, and the performance of the models produced is promising, with F-scores comparable to carefully selected manual models. We provide some perspectives to improve on these performances in future work.