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The verbal sparring is already under way, with Mr Cull and his closest mayoral rivals, Hilary Calvert and Cr Lee Vandervis, trading barbs yesterday.
Mr Cull plans to meet all new councillors in the coming days, and hopes a better understanding of council affairs by some will help heal any rifts.
Mr Cull was satisfied with the ''sound endorsement'' delivered by voters in Dunedin, which saw him romp home to win a second term as mayor with 18,446 votes.
That gave him a 12,017-vote margin over Ms Calvert, who garnered 6429 votes.
Trailing the pair were Cr Vandervis (5841 votes), Andrew Whiley (2946), Aaron Hawkins (2900), Pete George (779), Olivier Lequeux (503), Kevin Dwyer (217) and Steve McGregor (178).
Mr Cull believes the new council has the makings of ''a very constructive'' grouping, despite the return of one of his most vocal critics, Cr Vandervis, and the election of another, Ms Calvert.
Both launched repeated attacks on Mr Cull and the council's financial management during their mayoral campaigns.
Another incoming councillor, Doug Hall, remains locked in a legal dispute with the council over the State Highway 88 realignment.
Mr Cull said the diversity of views around the council table would be ''challenging'' but ''healthy'', and hoped for consensual decision-making.
That included Ms Calvert, despite her continuing criticism of council finances, he said.
''I think she'll find, once she examines things a little more thoroughly, that her concerns were misplaced.
''Since I'm sure she's not intending to be a single-issue councillor, I'm sure there will be lots of other things she can devote her energies to.''
He denied Ms Calvert's high polling as a councillor was a public rebuke of the council's financial management.
The state of the council's finances, and the council's awareness of the position, was ''the best it's been, probably for decades'', he said.
Ms Calvert disagreed yesterday, saying the results were not an endorsement of the council's financial management, which would remain a focus for her.
Instead, the healthy endorsement for Mr Cull reflected the lack of a major divisive issue such as the Forsyth Barr Stadium, she believed.
''This time [voters] weren't so dissatisfied, but that's not a ringing endorsement, I don't think.''
Cr Vandervis said he was disappointed ''Dunedin's biggest ever debt-spending mayor'' received more than double the votes of candidates with business experience, who wanted to reduce debt.
''Mayor Cull's excellent poll result confirms most people's acceptance of his practised TV host delivery, and his remarkable ability to sit on the fence, keep debt-spending and fail to offend anybody.''
However, the injection of new councillors with business experience suggested ''an awakening'' to the need for more careful financial management, Cr Vandervis said.
He predicted a ''challenging'' term as Greater Dunedin's candidates battled ''the rest'' of the council.
Mr Cull hoped the next three years would be more about implementing initiatives contained in the economic development strategy and the council's other planning documents, and less about the ''surprises'' of his first term as mayor.
He also denied Greater Dunedin's hand had been strengthened by Saturday's results, despite the election of a sixth member of the group - Mike Lord - and said there would continue to be no bloc voting.
''That's not what we're about ... I always aim to have a much bigger majority than just a couple of my mates.''
The new council will meet formally for the first time on October 29. Mr Cull said he would talk to councillors during the next few days to discuss appointments, roles and the committee structure.
Mr Cull has new mayoral powers to appoint his deputy mayor, committee chairmen and make changes to committee structures, unless a majority of councillors opt to vote against his decisions.
Changes to the committee structure would be considered, including reorganising the finance, strategy and development committee - created by a merger at the start of the last term - by removing the strategy arm, he said.
Issues of strategy could in future go to full council, given their importance, while steering groups and working parties might also become sub-committees to make them ''a little more formal'', he said.
It was likely Mr Cull's first-term deputy, Cr Chris Staynes, would continue in the role for a second term. A decision was likely within days, Mr Cull said.