This paper argues that it is necessary to allow for country-pair heterogeneity when using the gravity model to estimate international trade flows. We propose and estimate a fixed-effects model that eliminates the heterogeneity bias inherent in standard methods. Further, we show that there is no statistical support for the restrictions necessary to obtain existing empirical models, which are special cases of our model. Because the gravity model has become the ‘workhorse’ baseline model for estimating the effects of international integration, this has important empirical implications. In particular, our results suggest that standard gravity estimates of the effects of integration can differ a great deal from what is obtained when heterogeneity is accounted for. (JEL F15, F17)