We consider policy issues regarding parallel imports (PIs) of brand-name pharmaceuticals in the European Union, where such trade is permitted. We develop a simple model in which an original manufacturer competes in its home market with PI firms. The model suggests that for small trade costs the original manufacturer will accommodate the import decisions of parallel traders and that the price in the home market falls as the volume of parallel imports rises. Using data from Sweden we find that the prices of drugs subject to competition from parallel imports fell relative to other drugs over the period 1994 - 1999. Econometric analysis finds that parallel imports significantly reduced manufacturing prices, by from 12 to 19 percent. There is evidence that this effect increases with multiple PI entrants.