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However, the city may also have to accept a grim reality - the need to pick the most significant buildings and town precincts to protect, rather than trying to save everything, Mr Graham said.
Mr Graham said last month's partial collapse of the Rattray St building should focus attention on the need to be more proactive in protecting Dunedin's older buildings.
The city was unlike any other in New Zealand in the quality of its heritage building stock, and the precincts that collections of them clumped together created.
However, it appeared some people were guilty of taking for granted just how lucky the city was, including some building owners.
No complete audit of the city's heritage buildings existed, but it was clear from simple observation "there are buildings that are in a lot worse condition than other buildings", he said.
"That could be a reflection of age - it could be a reflection of the care they have had over time. There are some pretty obvious standouts where there's not a lot of care, and we can expect [more] situations like what happened in Rattray St."
The devastating effects of the Christchurch earthquake on that city's heritage buildings highlighted the need to move more quickly to upgrade Dunedin's.
Neglectful owners should have a responsibility to make a greater contribution towards the upgrade of their assets, but would benefit from an enhanced asset with the possibility of greater returns in future, he said.
Central government should also be contributing, perhaps through financial incentives that would serve to improve buildings and revitalise the local economy, Mr Graham said.
The council already contributed through the Dunedin Heritage Fund, rates relief and other incentives, but was considering other initiatives through its Heritage Buildings Economic Reuse Steering Group.
Mr Graham said the council could lead the way by changing its district plan to "set the foundation" and provide greater protection for heritage buildings.
Changes to the building code would also need to be considered.
At present, heritage buildings owners could be stifled by change of use rules, which required an investment in new systems, to protect against fires and earthquakes, once work to refurbish a building began, he said.
The work would be beneficial, but came at a cost that could be enough to put off owners.
The trust did not have the power to force owners or other organisations to act, and could not - by itself - provide protection for buildings.
The trust's approach was to work with owners and the council to offer advice, as a partner, on how best to handle particular buildings, he said.
Real changes to the rules protecting buildings would come from the council, through changes to its district plan.
"That might require a level of boldness," Mr Graham said.
He praised the success the city had enjoyed in protecting its most significant buildings, and listed examples of projects showing off the benefits of adapted reuse - from the Golden Centre to the Municipal Chambers and individual commercial buildings.
However, an incremental loss of heritage buildings was still taking place in other parts of the city, meaning "gaps" were slowly appearing.
"The southern end of Princes St is pretty gappy," he said.
Economic realities and stagnant population growth in Dunedin - together with expenditure on other capital projects - all combined to "create limits on what else can be done" for heritage buildings, he said.
That meant picking projects to focus on was key, based on a recognition of "what's achievable for us as a city".