We examine the quantitative predictions of heterogeneous firm models à la Melitz (2003) in the context of the Canada - US Free Trade Agreement (CUSFTA) of 1989. We compute predicted increases in trade flows and measured productivity across a range of standard models and compare them to the post-CUSFTA increases observed in the data. Our results point to a fundamental problem which most models we analyse face: predicted increases in measured productivity are too low by an order of magnitude relative to predicted increases in trade flows. Thus, most models are inherently incapable of simultaneously matching trade and productivity reactions to freer trade, raising doubts about the accuracy of the quantitative predictions of a large number of work-horse models in the literature. Using a multi-product firm extension of our baseline model as an example, we show that allowing for within-firm productivity increases has the potential to reconcile model predictions with the data.