The force has been moving more officers into community policing
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Police in Devon and Cornwall are considering taking on extra officers to avert action by detectives threatening to stop answering call outs to serious crimes.
Some detectives say their personal lives have suffered because of a recent spate of murder cases.
The force is considering how detectives' hours can be reduced.
They are considering taking on more officers, so extra staff can be moved into CID to spread the workload.
Recent investigations include the murder of parish councillor Peter Solheim in Falmouth and the murder of teenager Charlotte Pinkney in north Devon.
Fresh look
Assistant Chief Constable Tony Melville said: "The last few months has seen an unprecedented demand with 17 murders and major inquiries.
"Our detectives have been working tirelessly and tenaciously to bring 14 of those cases to a point where they are going before the courts.
"We need now to take a fresh look at the way we provide that kind of critical cover with detectives across the force."
The force has set a deadline of 1 November to resolve the dispute.
Recruiting more staff would probably mean an increase in the police's share of local council taxes for the third year running.
The force has been stepping up its demands on council tax payers as it moves more officers into community policing.
It currently has 3,460 officers and plans to increase that to 3,500.