Is it ever okay to "grease" an official's palm?
If the payment is only intended and only results in an official carrying out his or her job duties a bit faster (without breaking any other rules), then it MAY be legal. If the payment speeds up the process by ignoring the local laws or regulatory process, then the payment is still an illegal bribe. So in addition to the FCPA, you must check written laws of the host country. link
You can find many other sources, the case law around it is a bit nuanced, but basically if you're just trying to get stuff off someones desk that should be moving along under local law then you're probably ok. Congress obviously didn't mean to make it impossible for US based companies to do business around the world so the courts have to take that into account. Since most folks aren't lawyers practicing in that area of law corporate training tends to be very black and white on the issue (this also works to absolve the company if their employees tread into areas that are dark shades of grey).