Ann's concerns are legitimate about getting another credit card with a rate as good as the one she had. With a tightening of credit standards, she may have difficulty getting another credit card at all.

She has less to be worried about concerning her credit score because she does not have any other credit cards.

"A person's FICO score is influenced by everything in the person's listed credit history, so the impact of a change to one account will be strongly influenced by the other information on her credit report," said Craig Watts, public affairs director for FICO (formerly known as Fair Isaac Corp.), the creator of the widely used credit-scoring system.

What most affects a person's score when an account is closed is the presence of outstanding balances on other open credit accounts -- not the closure of the account per se. The scoring system looks at how much credit you are using compared with how much you have available.

So for example, if someone has three credit card accounts, all with zero balances, that person could close one of them with confidence that the closure won't change her FICO score, because it won't change her credit utilization rate, Watts said.

There's a page on FICO's Web site that discusses how closing a card account may influence a person's credit score.

Watts also cleared up a common misconception. Closing a credit card account won't affect the duration of someone's credit history. That's because credit reports include the history of closed accounts for a number of years following closure, and FICO scores consider both open and closed accounts when calculating the person's length of credit history.

So, deal or no deal for Ann?

Ann, tell your credit issuer you won't be played. Similar to the weary, downtrodden worker in David Allan Coe's song "Take This Job and Shove It," have the nerve to walk away.

Ann shouldn't be carrying $10,000 on her credit card, but she shouldn't stand for this treatment. She should pay off this debt -- and until she does, she doesn't need another credit card.

So Ann, don't take the banker's offer.

No deal.