"Gagging orders" have been issued to almost 240 ex-Devon County Council employees in the past five years, BBC News has learnt.
Almost £2.8m of public money has been spent on compromise agreements, which give staff a higher payout for not challenging their departure or speaking to the media.
The largest payout in 2008-09 was £57,374 compared to £123,810 last year.
The council said the 236 agreements reflected a cut in management roles.
'Reassure the public'
Ben Bradshaw, the Labour MP for Exeter, said such "gagging clauses have been widely discredited across the public sector" and Devon County Council should give a "full explanation for their continued use".
"It [the council] will also need to reassure the public that no-one has been paid more than their contractual entitlement and current contracts are being changed to avoid excessive pay-offs in future," he added.
Devon County Council said the total payouts, which were released under a Freedom Of Information Act request, included staff employed by the authority and those in maintained schools.
In a statement the Conservative-led authority said: "The increase was a reflection of the fact that the council has over recent years reduced its management by about a quarter.
"The increase in the largest individual amount paid is also a reflection of the seniority of the employees who have left."
It said the agreements contained confidentiality clauses that "restrict the employee from disclosing the details of the agreement itself" and from disclosing confidential data the staff member had access to during their employment.
"We have lost nearly 3,000 staff since 2009, and therefore the number of settlement agreements is a very small proportion of the number of people who have left our employment."
The authority added the compromise agreements did not "prevent employees from disclosing information regarding the practices of the council or schools".
In Torbay, the Conservative-controlled authority paid more than £550,000 on compromise agreements in a four-year period.
Since 2009-10 the number of agreements, which excluded maintained school staff, has increased from four to 13 in 2012-13.
Torbay Council is yet to comment on the figures.
Local government minister Brandon Lewis said: "We've been very clear that legal devices like non-disclosure or compromise agreements should not be used to reward failure or gag staff.
"Local government has a responsibility to the public and transparency is at the heart of that.
"How taxpayers' money is spent must be democratically accountable and open to scrutiny by the public.
"That's why I have asked all local authorities to increase transparency and accountability on severance payments."
A compromise agreement is reached after an employer and staff member disagree about a workplace dispute, resulting in the employee leaving with a payment combined with a confidentiality clause.
This means both the employer and employee should not speak publicly about their disagreement.
Labour-led Plymouth City Council said it did not "hold" the information in "electronic records or databases" and it would need to be "extracted from manual records" which would have exceeded the costs allocated to a freedom of information request.