A standard theoretical prediction is that average exports are independent of tariff rates when the underlying distribution of firm productivities is assumed to be the widely-used Pareto distribution. Assuming that the underlying distribution has no upper bound is undoubtedly inaccurate and produces theoretical results at odds with empirical results. In contrast, we show that upper-truncation of the Pareto distribution makes average exports rise with trade liberalization. This result is derived analytically, and is supported by simulations. We extend our analysis to the cases of lognormal and Fréchet distributions, which are also frequently used by trade economists. Our findings for lognormal and Fréchet distributions are qualitatively similar to the findings using the truncated Pareto.