This paper uses a newly available comprehensive panel data set for manufacturing enterprises from 2001 to 2005 to document the first empirical results on the relationship between imports and productivity for Germany, a leading actor on the world market for goods. Furthermore, for the first time the direction of causality in this relationship is investigated systematically by testing for self-selection of more productive firms into importing, and for productivity-enhancing effects of imports ("learning-by importing"). We find a positive link between importing and productivity. From an empirical model with fixed enterprise effects that controls for firm size, industry, and unobservable firm heterogeneity we see that the premia for trading internationally are about the same in West and East Germany. Compared to firms that do not trade at all two-way traders do have the highest premia, followed by firms that only export, while firms that only import have the smallest estimated premia. We find evidence for a positive impact of productivity on importing, pointing to self-selection of more productive enterprises into imports, but no evidence for positive effects of importing on productivity due to learning-by-importing.