Bristol should be run by an elected mayor, according to a Labour Peer who has criticised the way the city is run.
In a letter to the government about the Localism Bill, Lord Adonis said the system of governance in Bristol was "working particularly badly."
Liberal Democrat council leader Barbara Janke has written to the deputy prime minister to complain about Lord Adonis's comments.
Ms Janke said the report "lacked rigour" and the "facts were shaky".
Lord Adonis, a former schools minister, is the director of the Institute for Government, an independent charity which says it aims to improve government effectiveness.
He said Bristol had had seven leaders in the past 10 years.
"The big issue is can Bristol have a stronger, more effective, leadership if it goes to an elected mayor and doesn't have this constant instability in the council which is leading to poor services?
"An elected mayor would have a proper strategic plan for the city.
"[This] which would bring much greater focus, much greater energy and much greater corporate effort into improving services.
"Constant changes in administration [are] not good for strategic planning and not good for engendering confidence in the city."
Ms Janke said: "To have a peer of the realm coming here, making public criticism of our city and our schools based on a poor analysis is, in his words, 'deplorable'.
"I have worked pretty hard with business, universities, police, heath, to engender to the outside world a sense of confidence in Bristol so we can attract public and private investment.
"Jobs, prosperity, is what this city is about. We're a highly successful economy and we don't need people like this coming and undermining our confidence to the external world.
"It's very damaging and, in my view, we ought to have more responsible public figures than this," she added
A referendum is due to take place in the city next May, to choose whether a mayor should take charge.
Elected mayors are responsible for the day-to-day running of local services and serve for four years.
They provide political leadership to the council and the community and carry out the local authority's policies.