Greens MLA Caroline Le Couteur on Wednesday proposed the territory move towards a system used in Finland and other European nations, where a flat fine for minor offences is replaced with a tiered system based on people's capacity to pay.

In a motion passed by the Legislative Assembly, Ms Le Couteur also urged the government to write to all ratepayers who are provided concessions to tell them how they could defer rates bills, as well as publish the eligibility criteria for hardship claims for any residents.

She said while many in the city earned high average incomes, there was still a section of the community struggling to pay their bills, and many might not be aware of the options available. She said more than 80 per cent of driver licence suspensions were due to traffic or speeding fines.

Ms Le Couteur also said she would like the government to consider expanding the existing concessions system, which is based on a Commonwealth criteria that many people, such as those working on low incomes, were unable to access.

But Ms Le Couteur did not include widening the territory's concessions system in her motion, instead asking the territory government to pursue the federal government, through COAG, to find opportunities for state and territory governments to access Commonwealth support for low income concessions.

It would seem such an option is unlikely to be undertaken this side of the next federal election, given successive federal governments have failed to raise benefits for those on Newstart and other pensions in real terms for more than two decades.

Chief Minister Andrew Barr said he supported the motion, emphasising that the government earlier this year made changes to roads regulations to allow people to undertake payment plans or other options, and 32,800 residents had accessed one of those options since.

The government will now investigate the proposed changes. But with no specific date on which to report back on any findings of the investigation, it is unclear when the findings would be publicly available, and it would remain a government decision to adopt, or not adopt, the Greens' proposal.

While Opposition Leader Alistair Coe said he supported Ms Le Couteur's motion, he was concerned the motion did not fully take account of the effect of year-on-year increases in rates, fees, charges and taxes that hit all Canberrans regardless of their income.

He also raised concerns about how an income-tested fine system would work in practice, given such information was held by the Australian Tax Office and may lead to privacy concerns for those who felt uncomfortable about revealing their income.

But Ms Le Couteur said she believed most Canberrans had voted for the Labor-Greens government in 2016 knowing they would be paying more for services they expected, despite the increases, though she believed such changes could help those with less capacity to pay.