"Our team of seven arborists is working methodically, tackling the clean-up neighbourhood by neighbourhood," said Barrie.
"We're prioritising removing trees around powerlines, and those on private property, roads and footpaths.
"We'll clear entire areas as we get to them, however, every time a new report or intel of a dangerous tree comes in, council's team must move to assess the new risk."
Mayor Paula Southgate is full of praise for council staff and contractors for the non-stop work on the ground since the storm hit.
"Some of our people have worked extraordinary hours to get the city back into shape," she said.
"It's been really tough and sometimes dangerous work in the most challenging of circumstances. I know all Councillors are proud of what's been achieved already so I want to acknowledge all those involved, including staff behind the scenes. Our city appreciates it and I thank residents for their patience."
Council is asking residents to only report situations that pose a risk to people or property, and refrain from seeking updates on previously reported fallen trees.
"To remove a tree safely can take a whole day, and sometimes that also means we have to shut a road, which requires traffic management plans and approvals which all take time," said Barrie.
"This one event will mean weeks of unexpected work for our teams, on top of our business-as-usual responsibilities. Please know we're working to get to your street as fast as we can."