We present a gravity model that accounts for multilateral resistance, firm heterogeneity and country-selection into trade, while accommodating asymmetries in trade flows. A new equation for the proportion of exporting firms takes a gravity form, such that the extensive margin is also affected by multilateral resistance. We develop Taylor approximated multilateral resistance terms with which to capture the comparative static effects of changes in trade costs. For isolated bilateral changes in trade frictions, multilateral resistance effects are small for most countries. However, if all countries reduce their trade frictions, the impact of multilateral resistance is so strong that bilateral trade falls in most cases, despite the larger trade elasticities implied by firm heterogeneity. As a consequence, the world-wide trade response, though positive, is much lower.