The Renfrewshire households, which are affected by disability and illness, have been spared from a hit worth about £150,000 a year in total.
The council found that in the case of people who receive housing benefit, a so-called "spare room" is not, in fact, spare because it is needed as an additional space for an overnight carer or can't be used as a bedroom because it is needed for storing medical equipment.
Council leader Mark Macmillan said: "I am delighted that in the case of 263 residents facing illness or disability we have been able to re-assess their case.
"This will save these households on average an £11 cut in their housing benefit each week. That is about £572 over the year for each home.
"I have always maintained this benefit change is unfair, and we have now heard directly from UN official, Raquel Rolnik, that under occupancy rules should be suspended to allow time to assess the human rights implications and re-design the reform. I share her view.
"We will do all we can to help Renfrewshire residents who are facing hardship as a result of the 'bedroom tax'.
"I would encourage anyone who feels that their 'spare' room can't be used as a bedroom because of disability or medical reasons to contact our benefits team."
Renfrewshire residents who want to speak to someone about having a room re-assessed due to disability or medical equipment, or because of a overnight carer sleeping in a room, should call 0300 300 0204.
People who receive housing benefit and are having difficulty meeting their home costs can apply for financial support to the council's Discretionary Housing Payments fund by calling the same number of using the website: www.renfrewshire.gov.uk/dhp