Barclays, Lloyds, RBS and HSBC are now offering customers redress for the mis-selling, either in the form of cash or a new, more appropriate product.
This will be paid first, then an evaluation carried out to see if the firm is owed consequential losses from the mis-sold product.
That stage can take several more months, and initially the plan was to pay both parts at once.
Under the new setup the initial redress can be paid more rapidly.
Barclays and Lloyds are expected to focus on firms in financial distress first, while HSBC and RBS are not breaking down its list of customers.
The banks had come under fire from City Watchdog the Financial Conduct Authority (FCA) for being too slow to compensate customers.
“I welcome the moves to pay compensation in two stages,” said FCA chief Martin Wheatley. “I’ve been urging the banks to consider what more they could do to ensure the small businesses affected by swap mis-selling get the compensation they’re owed as quickly as possible.”