A council which caused outrage by flattening more than 600 headstones is to focus its efforts on older memorials.
Lewes District Council said the move would give time for families to make sure headstones were secure.
The council was accused of desecration after grieving relatives found contractors flattening unstable headstones.
Workmen identified unstable memorials to stop them becoming a danger to children playing in graveyards.
Two years ago, a six-year-old child was crushed to death by a falling memorial in Harrogate, North Yorkshire.
A council spokeswoman confirmed there was no record of any child being killed or injured in the Lewes area.
She said: "Over the next few weeks, the programme will concentrate on older memorials with visual checks to single out unstable structures.
"The majority of memorials that are unstable have been modern. Older memorials are mostly safe.
"The council is contacting the Guild of Stonemasons to express its concerns about the problems found with modern memorials and the remedial work that will be needed."
Stonemason Chris Groom, 43, of Richmond Road, Brighton, said: "The council needs to blame someone and it's completely out of order for it to point the finger at stonemasons."
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