Herefordshire Council and Hereford and Worcester Fire Service are to appeal against being capped over their council tax rises.
Councillor Roger Phillips, leader of Herefordshire Council, said that the cabinet-backed appeal was a 'formality' and lodged after advice from the Local Government Association.
Councillor Phillips said he still hoped that Whitehall would accept the council's compromise to save the £120,000 cost of sending out new bills should the appeal fail.
The compromise would see the £253,000 - or the equivalent of £3.80 off the average Band D bill - that the Government wants cut from the council's £175.5 million 2004/2005 budget 'frozen' for a year.
Herefordshire Council could then retain its original 8.9% council tax increase and see the £253,000 subtracted from what spending settlement it received from the Government for 2005/2006.
Hereford and Worcester Fire Authority unanimously agreed an appeal against its cap, which effectively shaves £2.3 million - or £7 off an average Band D bill - from its £26.7 million budget when it met on Tuesday.
Its chairman, Councillor Richard Udall, said he would resign rather than implement the kind of cuts and redundancies necessary.
Councillor Peter Jones, one of the Herefordshire members of the authority, said he would 'consider his position' if the cap went ahead.
"That is certainly an option. It's a matter of conscience," he said.
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