Energy supplier EDF has offered to pay £4.5m after Ofgem found it had breached its marketing licence conditions.
The package, to be paid into 70,000 accounts belonging to "vulnerable consumers", is the biggest of its kind.
In its investigation Ofgem found that EDF customers were sometimes given incomplete information about their contract terms and the way their direct debits were calculated.
It also said that opening statements by telesales agents, offering savings, were made before they knew the circumstances of the customer involved.
The package will include an automatic refund of £50 to households that recieved the Warm Homes Discount, and a payment of £1m to the Citizens Advice Energy Best Deal campaign.
EDF denied the payment was a fine.