While Inversion Transduction Grammar (ITG) has regained more and more attention in recent years, it still suffers from the major obstacle of speed. We propose a discriminative ITG prun-ing framework using Minimum Error Rate Training and various features from previous work on ITG alignment. Experiment results show that it is superior to all existing heuristics in ITG pruning. On top of the pruning frame-work, we also propose a discriminative ITG alignment model using hierarchical phrase pairs, which improves both F-score and Bleu score over the baseline alignment system of GIZA++.