Special measures must be used to take down the 248 multi-storey flats at Bellsmyre, Dumbarton, which were found to have "unexpectedly high" levels of asbestos.
The method of demolition, which has been approved by the Health and Safety Executive (HSE), has added an extra £1.3m to the demolition bill.
Now platforms called "mast climbers" will be put up around the four blocks of flats to allow contractors to remove the concrete surrounding the asbestos.
Once this has been done scaffolding will be put up to allow the safe removal of the material.
A spokesman for West Dunbartonshire Council said this method is the safest for both workers and people living nearby, adding that the demolition will be completed in time to allow construction of the new Our Lady and St Patrick's High School on the site, which is due to start in March.
Councillor David McBride, convener of housing, said: "We need to demolish these unwanted tower blocks using the safest possible methods for the local community and contractors.
"Our surveys revealed that the levels of asbestos were far beyond the normal content expected in buildings of this age and type and so we have had to revise our approach accordingly.
"I'm pleased that our new approach has been endorsed by the HSE and that the demolition can still be undertaken safely in time for the site to be ready for the construction of the proposed new Our Lady and St Patrick's High School."
Vice convener of housing, Councillor Lawrence O'Neill, said: "These blocks were not fit to provide our tenants with the modern standards they deserve and were rightly recommended for demolition.
"While the demolition cost is higher than expected, it will allow for the regeneration of a key council site and offer an exciting future to local community of Bellsmyre."
Meanwhile, hundreds of new affordable homes could be built in West Dunbartonshire if the council agrees a partnership with Cube Housing Association.
Discussions are to begin over plans for affordable homes at the sites of the former Bonhill Primary School, and at former school sites in Clydebank.
Land at Singer Street and Second Avenue in Clydebank and at Croft Street and Raglan Street, Bonhill, are also earmarked for development as part of a 10-year regeneration programme.
The proposal would see 393 social rented homes built, with the council given the rights for first lets of all the properties.
It would also create up to 300 jobs and training opportunities and safeguard up to 1000 construction jobs.