BOSTON — A pair of the nation’s largest banks have eased controversial overdraft rules for customers as the financial-services industry faces criticism over charging lucrative fees to boost sagging profits in the recession.

Chase, the retail banking unit of J.P. Morgan Chase & Co., on Wednesday said it was overhauling its overdraft policies “”to make them clearer and simpler and to give customers more control over their debit cards and the fees they pay.””

The changes include eliminating overdrafts for debit cards unless the customer opts in to overdraft services, and getting rid of overdraft fees if a customer’s account is $5 or less overdrawn, Chase said.

Overdraft fees on debit cards have come under fire recently on reports the banking industry is pocketing billions of dollars a year on the charges.

“”We recognize the tremendous growth in our customers’ debit-card usage and we’re revamping our overdraft policies and posting order to be more consistent with the way they use their accounts today,”” saidCharlie Scharf, head of retail financial services at J.P. Morgan Chase, in a news release Wednesday.

“”Customers will be given the opportunity to decide whether they want to participate in Chase’s debit-card overdraft services,”” he said.

The New York Times reported that Chase collects a customer’s debit-card and ATM transactions for a day and then processes the highest amounts first, creating more overdrafts and fees. By the first quarter of next year, the Times reported, the bank will process the transactions chronologically.

Bank of America Corp. late Tuesday unveiled a revamp of its checking-account options and services “”that will help customers avoid excessive overdraft fess and better manage their finances.””

The bank said that starting Oct. 19, it won’t charge overdraft fees when a customer’s account is overdrawn by less than $10 for one day. It will also “”improve the process”” for customers to opt out of overdraft capability.

“”Our immediate priority is those customers who excessively overdraw their accounts,”” saidSusan Faulkner, customer segments and deposits executive at B. of A.

“”With these changes, we have increased customer choice in the area of overdrafts, limited daily overdraft fees, and significantly reduced fees for those customers who need help the most.””

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