Consumers who received recorded phone messages from Npower could get compensation after the regulator found the energy giant guilty of breaching rules.
Ofcom has fined the firm £60,000 for the calls, made to a mixture of Npower and non-Npower customers.
Victims will receive a £10 Love2shop voucher, for high street stores including Argos, Boots and Debenhams. Npower says roughly 3,600 people will get a voucher.
The problem occurs when an automatic dialler system generates more calls than call centre staff can handle, so there is no-one from the company to take it. Instead, the company plays a recorded message.
What did Npower do wrong?
Ofcom found Npower broke the rules on eight days between 1 February 2011 and 21 March 2011.
Some calls would have played a generic recorded message. Only 3% of outbound calls in one day are allowed to be recorded messages.
Ofcom found Npower made 1,750 of these over its limit.
Npower also made 1,900 calls where the receiver heard a marketing message, which is completely against the regulations.
Npower is identifying who it made these calls to and will call or write to customers to offer them the voucher, depending on what details it has on file.
It will offer vouchers to all households who got a marketing message during the problem period.
For those who got a generic message, it will only offer a voucher to the 1,750 who got a call once Npower exceeded its 3% daily limit.
An Npower spokesman says: "We're sorry we made a number of calls in breach of our obligations. It is our responsibility to ensure we operate in accordance with Ofcom's rules."