You know the economy is bad when credit card companies start paying customers to close their accounts.

But that's what it's come to at American Express, which is offering some members $300 to go away.

Letters have gone out to an undisclosed number of customers "with sizable balances, with little account activity," according to American Express spokeswoman Molly Faust.

Faust described the voluntary program as "one of the steps we take to prudently manage risk based on customers' overall credit profile."

We think that means American Express singled out cardholders who are making minimum payments even though they're bouncing up against their credit limits, making them more likely to default.

Customers have until Feb. 28 to accept the offer, and another two months to pay off their balance. Once that's done, American Express will send a $300 prepaid gift card as their bonus.

Cardholders who accept the deal but don't pay off the balance by April 30 will still have their accounts closed and forfeit the bonus.

Participants also must redeem any membership reward points by then or they'll be lost when the account is closed.

Here's where to find all of our best advice on how to pay off credit card debt.