The closed and open economy literatures both work on evaluating the role of real rigidities, but in parallel. This paper brings the two literatures together. We use international price data and exchange rate shocks to evaluate the importance of real rigidities in price setting. We show that, consistent with the presence of real rigidities, the response of reset-price inflation to exchange rate shocks exhibits significant persistence. Individual import prices, conditional on changing, respond to exchange rate shocks prior to the last price change. At the same time, aggregate reset-price inflation for imports, like that for consumer prices, exhibits little persistence. Competitor prices affect firm pricing, and exchange rate pass-through into import prices is greater in response to trade-weighted, as opposed to bilateral, exchange rate shocks. We quantitatively evaluate sticky-price models (Calvo and menu cost) with variable markups at the wholesale level and constant markups at the retail level, consistent with empirical evidence. Variable markups alone generate price sluggishness at the aggregate level, while they fall short of matching price persistence at the micro level. Finally, variable markups magnify the size of the contract multiplier, but their absolute effects are modest unless they are coupled with exogenous sources of persistence.