But Mr Cull said yesterday any service cuts the council might make to produce savings would have to have "a lot of bang for their buck" before they were taken on board.
Council chief executive Jim Harland said yesterday while he would continue to work to find cost cuts and efficiencies, they could get to the point where they became politically unacceptable, as happened earlier this year when savings were considered for the city's libraries.
Mr Cull had his first day in the mayoral office yesterday, as he began to consult councillors on who he wants as deputy mayor and committee heads.
Mr Cull won office on Saturday after a campaign promising a more fiscally prudent council, and told Sean Plunket on TV3's political programme The Nation "efficiencies, in a word" was how he would cut spending without cutting services.
But council staff have said they were thorough this year when they looked for savings before the annual plan was produced.
A four-person team, for instance, interviewed every manager, asking them to justify their spending, and managed to cut what was a projected 8.7% rates rise to 7.3%.
After that, the council decided, among other initiatives, to alter the timing of some projects to spread the rates burden more evenly, and the final increase was fixed at 5.5%.
The city's annual plan shows an increase of 9.1% for 2011-12, 8.2% for 2012-13, 5.9% in 2013-14, and 5.5% in 2014-15, before the increases drop to 3% or lower in the next five years.
Mr Harland said yesterday the four-person team was still in place.
"We continue to do that work.
"Trying to find cheaper, more effective ways of doing things never stops."
Mr Harland said each council department had an activity management plan, and each of those had a "continuous improvement" section.
As well, there was a bonus system in place for staff that actively encouraged and rewarded ideas for improving processes and cutting costs.
Cost cutting could get to the point, though, where service levels were cut.
Asked if there were any more efficiencies to squeeze out of the council's system, Mr Harland said not all the ideas that had been raised at this year's annual plan had been picked up by councillors.
An example was a proposal to cut library spending by $300,000, from a budget of $10.2 million.
Library services manager Bernie Hawke said at the time any reduction would almost certainly result in a reduction of service levels, and councillors shied away from cuts at the time.
Mr Cull said yesterday he did not plan a special review to look for cuts; instead, cuts that "don't impact drastically on services" would be found, as usual, through the annual plan process.
"I suspect we would be duplicating things if we did [have a special review]."
Asked if he thought the council could have been more rigorous in its attempt to find savings at the libraries, Mr Cull said he did not think so.
"Libraries, we find, are hugely valued by the community, and utilised enormously."
The only situation savings may be acceptable, he said, may be where a library was open at a time when "there's nobody there".
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