Three Somerset councils have begun consultations on options for their leadership structures.
Mendip, South Somerset and Bath and North East Somerset councils are all reviewing their decision-making set-up.
New legislation requires councils to change their current structures to one of two models - a strong leader or directly-elected mayor.
Currently, the three authorities operate similar structures to the elected leader model.
South Somerset Council has said it is not keen on the mayoral option, partly because of the increased cost of an election.
Sedgemoor Council has said it will look at the proposals but has no plans to consult yet.
The deadline for responses is 26 November in Mendip, 19 November in South Somerset and 29 October in BANES.