This article presents the results we obtained on a complex annotation task (that of dependency syntax) using a specifically designed Game with a Purpose, ZombiLingo. We show that with suitable mechanisms (decomposition of the task, training of the players and regular control of the annotation quality during the game), it is possible to obtain annotations whose quality is significantly higher than that obtainable with a parser, provided that enough players participate. The source code of the game and the resulting annotated corpora (for French) are freely available.