Not long ago, it took multimillion-dollar payments delivered by corporations to lofty government officials to get the attention of the U.S. Department of Justice.

The Foreign Corrupt Practices Act, enacted in 1977, but not taken very seriously until just a few years ago, seemed to have a simple checklist of what would trigger prosecutions: Large precontract payment? Check. Offshore, numbered account? Check. Vast contract award? Check — and prosecute.