While the future shape of most Suffolk councils is now becoming clear after this month's elections, who will run Babergh remains uncertain.
The Green Party won 10 of the council's 32 seats, making it the largest single group. There are nine independents, seven Conservatives, five Liberal Democrats and a single Labour councillor.
The Greens hope that their position as the largest party will give them the lion's share of cabinet posts.
But other parties are concerned because only one Green has previous council experience - nine were elected for the first time on May 4.
Green councillor Deborah Saw said: "We are the largest party and we have been meeting regularly to get something sorted out."
A new administration has to be approved by the council's annual meeting next Tuesday evening - and it could be that discussions continue until then.
One Independent councillor said the talks were being very slow and it was frustrating that no clear path towards an administration had emerged.
In Babergh the personalities of councillors are as important a factor as the political labels they wear - and this also appears to be a factor.
Liberal Democrat group leader Lee Parker said meetings were taking place every day and progress was being made.
He said: "I think we are all aware of the importance of Tuesday's meeting. We are seeing what the others are saying and are hoping to act as an honest broker to try to bring them together."
It is not unusual for Babergh council's leadership to decided after the elections have taken place - in the 50 years since the first council was elected only once, in 2015, has a single party won a majority in an election.
And on that occasion the ruling Conservative group later split over proposals to merge with Mid Suffolk.
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