Landlords will be able to give tenants just one week's notice to leave the asbestos-contaminated houses under the buyback. Tenants will be able to leave with just two days' notice.

Mr Barr will also strengthen rules to ensure people don't sell a Fluffy house after the buyback offer closes at the end of June without buyers knowing its status. The Fluffy status will become searchable on the Land Titles register, adding another layer of disclosure.

Also in Thursday's package of changes, the government will legislate to allow Fluffy owners who signed up to the government's generous feed-in tariff for solar panels to keep the payment when they move to a new home.

The Asbestos Taskforce said it was still unsure how many Fluffy owners had signed up to the 50.5¢-a-kilowatt-hour scheme that closed in mid-2011, but in all 102 had solar panels.

Mr Barr said there would be no compensation paid to ActewAGL and other electricity companies for keeping the Fluffy owners in the scheme, but nor was there any extra cost to the companies. Fluffy owners are being allowed to take solar panels with them if they were installed after July 2013 and meet current fire rules.

Mr Barr confirmed the list of Mr Fluffy homes would be made public in the last week of June.

A register of houses was required to allow the mandating of asbestos management plans for these properties, attachment of new planning permissions and the the capacity to break residential tenancies, he said.

Tenants already have access to the relocation allowance being paid to owners, of $10,000 a household, plus $2000 for each dependent child. Landlords can get a $5000 lump sum.

The government had made nearly 500 offers under the buyback scheme, and now owned about 75 properties. The legislation to be tabled on Thursday will scrap the need for building and pest inspection, and energy rating reports when homes are sold to the government under the buyback.