The US' Foreign Corrupt Practices Act[0] has, for example, done wonders. The US had decided that it wouldn't allow its domestic companies to bribe foreign officials. And because they were (legitimately) afraid of losing business to countries with lax standards, they expanded its power to foreign companies.
Until the late 90s, for example, most European countries allowed the tax deduction of foreign bribes. Yeah, it wasn't just legal, but tax-supported. That changed dramatically with the FCPA, and actions such as Airbus' are now the exception rather than the norm.
It's similar in politics, where I think people vastly overestimate the number of money-filled suitcases changing hands.
The problem today is a different form of political corruption, namely that which has been legalised by Citizens United.
[0] https://en.wikipedia.org/wiki/Foreign_Corrupt_Practices_Act