The sitting Plaid Cymru councillor, John Crossley, chose to contest Llangeler and the party did not field a candidate, leading to the loss of the seat to the Independents.
The elected candidate, who had sat as a Ratepayer for Gorslas since 1995, and on Dyfed County Council since 1977, had now joined the Independent group.
Osi Rhys Osmond had been elected at a by-election following the death of the previous Independent councillor, Arthur Harries.
He then chose to contest Llwynhendy alongside sitting Independent councillor Don Davies, who had himself been de-selected by Labour prior to the 1999 election.
Joy Williams captured the seat for Plaid Cymru at a by-election following the death of the previous Independent Labour councillor, Ieuan Edwards.