Anderson and van Wincoop (2003) showed the importance of multilateral resistance general equilibrium effects in estimating the response of trade flows to trade costs. We integrate this into Helpman, Melitz, and Rubinstein's (2008) extension of Anderson and van Wincoop's framework, which allows for firm heterogeneity, in order to quantify the different margins of adjustment. For bilateral trade cost changes, the general equilibrium effects are small. Surprisingly, most country pairs reduce their trade after a multilateral fall in trade costs. The global trade response to lower costs is positive, amplified by firm entry, but significantly dampened by multilateral resistance.