Whenever the invisible hand isn't operating the iron fist is

We'll hold out our hand; they have to unclench their fist.

He's got an iron fist when he needs to, but he knows when to hold off. He's got a good mix, and he does very well with the players.

Iron hand in a velvet glove.

In economy, invisible hand is a set of wealthy men. It's the puppeteer who's in charge behind the curtain.

John is an iron fist in a velvet glove, ... He's every bit as determined and tenacious as he is uplifting and gracious. He's a skilled manager of people, he's well-respected by my staff and Cabinet, and he knows how to cut to the quick of solving a problem. He's the kind of professional - and friend - I trust to offer smart counsel and honest input in every situation.