In this paper, we examine the extent to which market structure and the way in which it affects pricing decisions of profit-maximizing firms can explain incomplete exchange rate passthrough. To this purpose, we evaluate how pass-through rates vary across trade partners and sectors depending on the mass and size distribution of firms affected by a particular exchange rate shock. In the first step of our analysis, we decompose bilateral exchange rate movements into broad US Dollar (USD) movements and trade-partner currency (TPC) movements. Using micro data on US import prices, we show that the pass-through rate following USD movements is up to four times as large as the pass-through rate following TPC movements and that the rate of pass-through following TPC movements is increasing in the trade partner's sector-specific market share. In the second step, we draw on the parsimonious model of oligopoly pricing featuring variable markups of Dornbusch (1987) and Atkeson and Burstein (2008) to show how the distribution of firms' market shares and origins within a sector affects the trade-partner specific pass-through rate. Third, we calibrate this model using our exchange rate decomposition and information on the origin of firms and their market shares. We find that the calibrated model can explain a substantial part of the variation in import price changes and pass-through rates across sectors, trade partners, and sector-trade partner pairs.