But the majority were persuaded by funeral directors' enthusiasm for the upgrade and larger seating capacity, and an assurance that there would be demand for two competing facilities.
The existing council crematorium's chapel was closed in 2012 when it received a 29 per cent earthquake code rating.
It was reopened in 2013 after remedial work but the complex requires further strengthening and a general upgrade.
Meanwhile councillors at yesterday's meeting also approved the next steps in an "engagement plan" to consult the public over the options for the future of the Opera House and Municipal building complex, large parts of which were closed last year after engineers identified structural issues.
The council intends running a public consultation process to consider seismic strengthening options for the complex, alongside plans for an upgrade to Civic Square and the development of a CBD hotel in the city.
All three projects were initially expected to cost a total of $20 million, but a larger than expected estimate for the opera house work means that decisions now need to be made on which projects proceed.
The council's engagement plan - ahead of it making a decision scheduled for November 26 - includes putting a "short list" of options out to the community by July. That will be ahead of a formal consultation process which is to begin in September.
A report prepared for yesterday's meeting said the formal consultation process was likely to include setting up a "mini expo" in the Opera House Plaza as well as information evenings and information distributed to households.
An external working group is due to prepare an initial short list of options, along with details on the risks, benefits and cost of each option.
Mayor Lawrence Yule said there would be a process to present those options to the public.