Applied General Equilibrium (AGE) models are the dominant tool for the analysis of trade policy. Unfortunately, AGE models have historically performed poorly when used to predict the industry level impact of trade liberalization. We develop a flexible methodology for estimating industry level trade elasticities based on finding the elasticities that yield AGE model predictions that best fit previous liberalizations. We show that these elasticities yield significantly improved predictions in tests of external validity, in part because they implicitly capture the extensive margin growth of least traded products (LTPs) from Kehoe & Ruhl (2013), which occurs during liberalization. We show explicitly including the LTP margin further increases the predictive power of AGE models.