GONE are the days when multinationals could book bribes paid in far-flung countries as a tax-deductible expense. These days would-be palm-greasers have to contend with ever-tougher enforcement of old laws, such as America’s Foreign Corrupt Practices Act of 1977, and a raft of new ones in countries from Britain to Brazil.

As policing is stepped up, however, much about the practice of bribery remains murky. The OECD’s first report on the subject, published on December 2nd, sheds some light by analysing more than 400 international bribery cases that have been brought since the anti-bribery convention of this group of mostly rich countries came into force in 1999.

Some findings confirm what was known or suspected. The most briberiddled sectors are oil, gas, mining, construction and transport. At the other end of the spectrum, financial services and retailing are fairly clean. Most bribes go to managers of state-owned companies, followed by customs officials. And America leads the enforcement pack, with 128 cases that resulted in sanctions (see chart).

But the report also undermines some common beliefs. Bribery is not a sin of rogue employees or poor countries. In 53% of cases payments were made or authorised by corporate managers (and in 12% of them by the chief executive). More than 40% of the time, the bribe-taking official was in a developed country (though this figure is probably inflated by rich countries’ greater willingness to criminalise bribery and co-operate with cross-border investigations). Authorities are often alerted by firms themselves: those that co-operate quickly are often treated leniently.

Nevertheless, the cleanest countries tend to be rich, and the dirtiest poor. Four of the five best-performing countries in Transparency International’s latest corruption-perceptions index, also published this week, were Nordic. The worst were North Korea and Somalia. (Interestingly, China’s score slipped despite a recent high-profile campaign against corrupt officials.)

The cost of bribery varies by industry. Builders pay a modest average of 4% of a transaction’s value, extractive companies a hefty 21%. Add to that the rising costs of paying penalties and conducting internal probes—these cost Siemens, for example, $2.4 billion when it was mired in a graft scandal a few years ago—and bribery starts to look bad not just for reputations, but also for bottom lines.

Even for firms that are not caught, the business case for bribery is far from clear. A 2013 study by Harvard Business School and America’s National Bureau of Economic Research found that what bribe-paying companies gain in higher sales in corrupt countries, they lose in lower profit margins. According to the OECD, the average bribe costs 11% of the transaction’s value and 35% of associated profits.

Nevertheless, graft remains alive and well. One of the OECD report’s authors told a conference this week that 390 cases are under investigation—not far short of the total number resolved since the OECD convention took effect 15 years ago. The number of cases concluded each year has dipped since a peak in 2011 as the time taken to complete investigations and prosecutions has climbed to more than seven years, from under four in 2008.

One possible reason for the slowdown is that bribery techniques are growing more sophisticated and thus harder to detect. Another could be the widespread use of opaque corporate structures to conceal wrongdoing. These can be devilishly difficult to unpick, especially when they are stacked in several layers and fronted by nominee directors. Anonymous shell companies and other intermediaries—sometimes dressed up as “consultants”—were used to move or to house payments in more than 70% of cases. The OECD report underlines the importance of cracking down on the misuse of shell companies and enforcing more clarity over ownership of companies and trusts, whether through accessible corporate registers—a move being pushed by some G20 countries, led by Britain—or by tougher regulation of service providers that do the paperwork for new firms.