Tree-to-string systems (and their forestbased extensions) have gained steady popularity thanks to their simplicity and efficiency, but there is a major limitation: they are unable to guarantee the grammaticality of the output, which is explicitly modeled in string-to-tree systems via targetside syntax. We thus propose to combine the advantages of both, and present a novel constituency-to-dependency translation model, which uses constituency forests on the source side to direct the translation, and dependency trees on the target side (as a language model) to ensure grammaticality. Medium-scale experiments show an absolute and statistically significant improvement of +0.7 BLEU points over a state-of-the-art forest-based tree-to-string system even with fewer rules. This is also the first time that a treeto-tree model can surpass tree-to-string counterparts.