The approval will imply individuals dwelling in Band D properties in Cheltenham should pay £252.11 per 12 months, up from £244.79 at the moment.
Jeffries stated the necessity for providers has elevated, however funding stays fragile for native authorities.
“I will not pretend that the national system is not broken,” he stated.
“We must be honest, district councils cannot keep absorbing rising costs.
“This price range is prudent, however passive; it is cautious however not caught.”
Meanwhile, the 2.99% increase in Gloucester will result in those in band D properties paying more than £244 over the year from April.
Councillors approved the council’s £27.7m budget, which would save the authority from having to issue a section 114, declaring it effectively bankrupt.
The approval of the price range comes days after the council was given permission by the federal government to promote a few of its property and borrow money to help fill a £15.5m blackhole.
Councillor Jeremy Hilton, Gloucester City Council, said in the meeting that the council had been “squeezed and squeezed and squeezed” financially in recent years.
He also said the financial crisis the council found itself in was “complicated and extreme”.