TORIES say the borough council is playing 'musical chairs' with its committee system.
After spending two months operating under the old system, the Conservatives proposed two alternative schemes to full council.
One of these suggestions was accepted at the meeting, with a minor amendment.
The Liberal Democrats proposed their own scheme, while the ruling Labour group didn't come up with any suggestions.
Tory councillor Gareth Anderson said afterwards: 'We argued that the old system, which Labour proposed to continue with, was proportionally unfair.
'And we say it had dubious legal basis, leaving the committee system proportionality open to judicial review.'
The main thrust of the Tories' difficulty with accepting the old system was centred on Labour's five extra committee seats.
The Conservatives also pointed out the 'disproportional seating' on the Highways Committee (83% Labour, 17% others).
Fellow Tory councillor for Led-sham ward Jonathan Starkey asked the council why there was 'such an apparent effort to keep proportionality out of the Highways Committee'.
He said it was the only ruling group in Cheshire not to do so. To date, he says he hasn't received an answer to this.
Cllr Anderson added: 'Labour failed to meet the opposition over the matter. But we were willing not to oppose the amendments put forward by Labour to our scheme so a less-than-perfect compromise would have full council approval, thus ending an unfair and imperfect system.'