The council revealed in December that the cost of the redevelopment,which has been frustrated by heritage concerns and delays to the council's previously published timeline for the project,hadballooned by $6 million.
North Sydney Mayor Jilly Gibson said the Milsons Point pool had"served our community splendidly for 84 years"after opening in 1936 and appointing a builder was"the best new year present"for residents.
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"The pool is being transformed from a lap-swimming pool to a pool for the whole community,"she said.
Councillor MaryAnn Beregi was concerned some councillors had not seen the contract or a probity plan for the project. She found out a builder had been appointed via an announcement on the council's website this month.
"The council's budget for the project has gone from $28 million to $58 million to $64 million,and we don't even know what $64 million will get us,"Cr Beregi said.
"I've been concerned by what I've read about[Icon's] financial position and the status of various legal claims,and whether they have sufficient experience to undertake what is an incredibly complex build on a heritage site."