At present, the council has operational control over only 15 per cent.
A possible way to do this is through a joint-venture with the main landfill and waste transfer station owners.
Councillors decided this on the basis of information presented in an official waste assessment paper.
However, Mr Franks said the paper gave councillors no appreciation of the costs and risks.
"There is concern that the assumptions about savings are not able to be substantiated.
"It's a curious order in which to do things - to adopt a strategic direction and put a strait-jacket around your options and then say you will do the analysis."
Waste and Recycling Council members wanted the council to reconsider and "look coldly" at the risks and whether there was a problem.
"You've had a 20 per cent reduction in waste over the past couple of years ... that's extraordinary."
Members urged cutting waste going to landfill by, for example, measures to separate food waste at the kerbside.
After Mr Franks' appeal, councillors Chris Fletcher and Cameron Brewer successfully sought a council resolution that officers ensure that interested waste industry leaders be invited to attend a consultation on the draft waste minimisation plan.
Councillor Mike Lee reminded members that ratepayers paid $84 million a year for waste disposal.
They, too, deserved a fair and objective consultation programme about how to reduce waste and ensure their money was spent as efficiently as possible.
The council's manager of infrastructure and environmental services, John Dragicevich, said the waste assessment had been updated to give the council confidence that it was proceeding on a sound basis.
He said the council needed a new waste minimisation bylaw by October next year when the present one expired A draft plan will go out for public consultation early next year.
