Also a lot of tact. If you just leave a check on somebody's desk, you're calling him a crook, and few crooks enjoy being called crooks; it works better to hire a politician for a speech somewhere, or offer him a seat on a board of directors or a well-paid job with a charity when he leaves office, or put in a word on his children's behalf with the director of an exclusive private school, or something like that...

The Saudis make an absolute art form of this, acting as a patron to the whole of DC. There are some memorable books about this.

There's an old folk belief in the Anglosphere, that the rich are less corruptible than the poor. (In 16th-century England, the legal definition of "an honest man" was one who had an income from land and investments of ten pounds or more: maybe equivalent to $100,000-$400,000 today.) This belief isn't true, at least not most of the time; but the art of deniable bribery gives a hint of where it came from.