Discriminative training methods have recently led to significant advances in the state of the art of machine translation (MT). Another promising trend is the incorporation of syntactic information into MT systems. Combining these trends is difficult for reasons of system complexity and computational complexity. The present study makes progress towards a syntax-aware MT system whose every component is trained discriminatively. Our main innovation is an approach to discriminative learning that is computationally efficient enough for large statistical MT systems, yet whose accuracy on translation sub-tasks is near the state of the art. Our source code is downloadable from http://nlp.cs.nyu.edu/GenPar/.