The board had said that charities would have to value 'heritage' assets, such as the Rosetta Stone in the British Museum or stately homes in the care of the National Trust, despite the difficulty and cost involved.
But it has now said such assets will need listing only if they have a purchase price or prior valuation.
"We carried out two consultations and are confident we've got it right," said Andrew Lennard, research director at the ASB. "But we're holding one more to check there's nothing we've missed."
The new consultation, FRED 42: Heritage Assets, is available at www.frc.org.uk/asb/publications and finishes on 10 October.