Yorkshire Building Society is offering two Mig-free products up to 95 per cent loan to value.
It is giving borrowers the option of a product without a Mig but with a higher interest rate or a product with a lower rate and a Mig.
A four-year cap at 7.35 per cent and a five-year fix at 7.09 per cent up to 95 per cent loan to value are both Mig-free.
If customers opt to pay a Mig, they can take a four-year cap at 6.99 per cent or a five-year fix at 6.79 per cent. The Mig is £895 on a £50,000 loan.
The society is not abolishing Migs across its range, unlike banks such as the Halifax and Abbey National.
Yorkshire communications manager David Holmes says: "We do not believe there is a huge demand for Mig-free products so we are testing the market. Converters will be costing in the free Migs somewhere. There is no such thing as a free lunch."
Redemption penalty on all four loans is 3.5 per cent for years one to three and 2.5 per cent for years four and five.