The goal is to weed out the latter groups to identify consumers whose credit scores are blemished but who still have the money to pay their bills.

“Lenders want to prove to themselves that it is worth taking a higher risk,” said Brad Jolson, an executive of the decision management company FICO, who has helped several card companies analyze their customer base.

This new approach to assessing default risk is emblematic of the challenge faced by the many banks that were hobbled by the financial crisis: They desperately want to grow again, but the memory of a near-death experience makes them wary about taking outsize risks.

Lenders have taken $189 billion in credit card losses since 2007, according to Oliver Wyman Group, a financial consultancy. That was a significant part of the $2 trillion or so that banks are estimated to have lost since the crisis began, and a contributor to the government bailout of the banking system.

To stem losses, lenders halted new card offers to all but their most affluent customers. At the same time, more than eight million consumers stopped using their credit cards, in a sign of the nationwide belt-tightening, according to TransUnion, the credit bureau. Millions more borrowers who still have cards have been compelled to pay down their balances, or are more often choosing to use cash.

That has had a big impact on lenders’ bottom lines. Credit cards once gave the banking industry as much as a quarter of its profits; today those profits have all but vanished and lenders are seeking ways to replace them.

Now that the losses have stabilized, lenders have set out to revive their card businesses, and mail offers to riskier borrowers are roaring back.