Call it the free-toaster offer in reverse.

Card issuers have retreated from the incentive-based customer acquisition strategies of recent years, to the point where one — American Express Co. — is paying cardholders to close their accounts. And another — Citigroup Inc. — is moving in the same direction. Observers said this could be an effective new risk management strategy — depending on how delicately it is implemented.

This month Amex offered a $300 prepaid debit card to what it called "a very small number of cardholders," if they agree to close their accounts by Saturday and pay down their remaining balances by the end of April.

Analysts predicted other issuers would soon follow suit.

"What Amex is trying to do is get first dibs" on being paid off, said Red Gillen, a senior analyst at Celent, a research arm of Marsh & McLennan Cos. Inc.'s Oliver Wyman. "I wouldn't be surprised if another lender takes the same approach."

Molly Faust, a spokeswoman for Amex, said the New York card company made its "one-time offer" to certain consumer credit cardholders "who have accounts with sizable balances and very little activity on those accounts, both in terms of spending and payment." She would not say whether the cardholders were current or delinquent.

Citi, meanwhile, is offering a credit of up to $550 to certain holders of its Sears MasterCard by matching 20% of any amount they pay above the minimum for four months. (The total match is capped at $550.) Citi is not closing the affected accounts but is freezing them while cardholders pay them down. A spokesman for Citi said it is "continuously developing and refining" programs for cardholders facing financial difficulty.

Other issuers, many of whom already offer incentives to cardholders for making payments above the minimum on large balances, left the door open to the possibility of rewarding those who leave.

JPMorgan Chase & Co. said it does "not have such a program at this time." Bank of America Corp. said it does not "currently offer buyouts," and Discover Financial Services said, "We are constantly evaluating how to best service our higher-risk accounts but currently are not offering a program similar to Amex." A spokeswoman for Capital One Financial Corp. said "nope" when asked whether it offers such a program.

Mr. Gillen warned that a proliferation of such offers could send a "confusing message" by seeming to reward nonpaying customers. If consumers see multiple chances to be rewarded for landing and then closing their accounts with an issuer, "what if you start shopping around your bad debt?" he said. "This could set a really bad precedent."

Rick Wittwer, a former card collections executive, called Amex's offer an "ingenious" variation on tactics his teams at Washington Mutual Inc. and Providian Financial Corp. used to encourage delinquent cardholders to pay down their accounts.

"We had these clocks made up, I think they cost us three dollars, and they got us payments," he said. "You had to keep mixing it up. For a while we tried movie tickets and then we tried gas cards — each one actually showed an increase in payment over the control."

It is more unusual for an issuer to approach cardholders who are not yet delinquent, he said, even if they have been late payers in the past. "You have to be careful about trying to collect too early because then you just tick them off and then they become nonperforming assets."

Still, cardholders who get the mailing "might be curious about why American Express doesn't want them as a customer anymore," Mr. Wittwer said, "but they won't be as upset as receiving a collections call while they're current."

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