Provider Rothesay Life is offering 65,000 customers transferred from Aegon and Zurich the possibility of swapping their annuity for a cash lump sum.
So far, the annuity provider has written to 40,000 clients, receiving "a very positive response", said Kathryn Jones, actuary at Rothesay Life.
The annuity provider's decision stems from the introduction of pension freedoms in April 2015, which made it possible for policyholders to take their benefits as a lump sum at retirement up to a certain limit established by HM Revenue & Customs (HMRC).
However, clients who purchased an annuity previous to this date weren't able to do this.
Ms Jones said: "This meant that the populations that were transferred to Rothesay from Aegon and Zurich contained a number of policyholders with small pensions in payment."
After taking "comprehensive legal advice" on the possibility of offering a cash lump sum to these policyholders, Rothesay Life started writing to eligible Aegon and Zurich policyholders who weren't given this option when they retired, she noted.
Ms Jones explained that mailings are being sent to those aged between 55 and 80, who have Aegon or Zurich benefits with a value of less than £10,000, the current limit established by HMRC.
"Those aged 80 to 85 are also being sent a letter to advise them of the process, giving them the option to opt-in to receive a pack if they wish," she added.
Policyholders have around 11 weeks to accept the offer of a lump sum, and the deadline is detailed in their pack.
There is a cooling-off period of two weeks after Rothesay Life receives their decision form.
If they don't respond, their pension payments will continue as normal, Ms Jones added.
The gross value of the lump sum has been calculated as the current value of the payments the provider would expect to make to an average policyholder according to his/her age over their lifetime, she said.
The option packs are being sent in batches to the relevant customers, since Rothesay Life wants to ensure receive the right level of service, such as maintaining customer service levels.
Around another 25,000 packs will be sent in 2019, Ms Jones concluded.
Royal London conducted a similar exercise recently, where more than 10,000 customers accepted a bonus to trade in their guaranteed annuity rates.