This is the first paper to empirically examine whether the United States' imposition of a special import restraint distorts foreign exports and thus affects world trade flows. We first develop a theoretical model of worldwide trade in which the imposition of a special import restraint by one country - an antidumping duty or a safeguard measure - causes significant distortions in world trade flows. We then empirically test this model by investigating the effect of US special import restraints on Japanese exports of roughly 3500 commodities into 29 countries between 1992 and 2001. Our estimation of a fixed-effects model of Japanese exports yields evidence that US import restraints both deflect and depress Japanese export flows. Imposition of a US antidumping duty against Japan deflects trade: export growth to non-US trading partners rises by 11 to 22 percentage points. The simultaneous imposition of a US antidumping duty against both Japan and a third country depresses trade: Japanese export growth to the third country falls by 0 to 18 percentage points. The magnitude of the trade depression effect is also larger when the US imposes an antidumping duty against a third country but not against Japan. A US safeguard measure leads Japanese export growth to third countries to rise 12 to 15 percentage points.