Wallingford Town Council wants warning notices put on the town's historic bridge over the Thames to stop people jumping off and injuring or killing themselves.
But the council will have to wait until a new by-law is made official, said mayor Theresa Jordan.
Then any jumpers will be in danger of prosecution, she said.
She wanted a notice placed on the parapet now saying: "Jumping off this bridge is dangerous."
But member Adrian Payne said it should read: "Don't be so bloody silly -- get off the bridge."
Ms Jordan said: "Bridge jumping has been going on for donkeys' years.
"But it is a dangerous sport -- young lives have been lost. We cannot just ignore the problem.
"We must keep trying to impress the dangers upon these youngsters."
New signs will be placed in the lavatory block in adjacent Riverside Park warning people of the dangers of bridge jumping.
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