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We document that delivery lags and transaction-level economics of scale matter for international trade, leading importers to import infrequently and hold additional inventory. In a model with these frictions calibrated to empirical measures of inventory and trade lumpiness, these frictions have a large (20 percent) tariff equivalent, mostly due to inventory carrying costs. These frictions also alter the dynamics of imports and prices. Consistent with evidence from large devaluation episodes in six developing economies, following terms-of-trade and interest rate shocks, the model generates a short-term implosion of imports and a gradual increase in the retail price of imports. (JEL D92, F14, G31, L81, M11)