In 2016, Brazilian construction rm Odebrecht was ned $2.6 billion by the US Department of Justice (DOJ). According to the plea agreement, between 2001 and 2016 Odebrecht paid $788 million in bribes in 10 Latin American and two African countries in more than 100 large projects. The DOJ estimated that bribe payments increased Odebrecht's pro ts by $2.4 billion. Judicial documents and press reports on the Odebrecht case reveal detailed information on the workings of corruption in the infrastructure sector. Based on these sources we establish ve facts. First, for projects where Odebrecht paid bribes, renegotiations amounted to 71.3 percent of initial investment estimates, compared with 6.5 percent for projects where Odebrecht paid no bribes. Second, Odebrecht's bribes were of the order of one percent of a project's nal investment. Third, the pro ts Odebrecht obtained from bribes as well as its overall pro ts were small, somewhere between 1 and 4 percent of its sales. Fourth, the creation of the Division of Structured Operations (DSO) by Odebrecht in 2006 led to major reductions in the rm's costs of paying bribes and recipients' costs of hiding the ilegal proceeds. Fifth, following the creation of the DSO, Odebrecht's sales increased more than threefold while its pro ts remained small. We build a model where rms compete for a project, anticipating a bilateral renegotiation at which their bargaining power is larger if they pay a bribe. Conditional on paying a bribe and cost dispersion among rms being small, rms' pro ts are small in equilibrium. When one rm unilaterally innovates by reducing the cost of paying bribes, its market share increases substantially while pro ts, which are proportional both to the cost advantage and to the magnitude of bribes, remain small. A parametrization with the DOJ's data suggests that Odebrecht enjoyed a substantial cost advantage in bribing, of the order of 70 percent.