Just 5,100 homes will get a waiver from paying the levy, compared to 43,000 properties that were not liable for the household charge.
It means that of the 1,770 unfinished housing developments around the country - residents in only 421 will not have to pay the new fee.
Minister Burton said that homeowners who believe they should be entitled to a deferral of the charge should outline their reasoning on the tax forms.
"If people have queries the they should take them up with the Revenue Commissioners, with the Department of Finance, and the Minister for Finance, because they will deal with any such queries," she said.
"Obviously as well if somebody is living in a property which is impaired because of its surroundings, I would expect that the valuation in that case would be very, very modest indeed."
The full list of exemptions can be found here.