The City of Vincent says three vicious dogs it has declared dangerous may attack again but the council has no power to destroy them immediately.
The dogs were responsible for brutal attacks on people and dogs in Perth's northern suburbs late last year.
Their owners were served council notices this week declaring the animals dangerous and the dogs will be euthanised if they attack again.
The notices require the owners of three Staffordshire bull terriers - two at a communal lodging in Highgate and the other in Mt Lawley - to adhere to strict requirements or face legal action.
The Highgate dogs seriously injured two people in separate attacks at the lodging, which left the victims needing medical treatment for cuts to their arms.
"Both of them are very aggressive and we think it will be a matter of time before they attack again," council chief executive John Giorgi said. "The dog owner has not been co-operating. The concern we've got there is that if the dogs get out in the street, they'll definitely do some damage."
But without a push by the victims for prosecution, the strongest action the council could take in this first instance was declaring the animals officially "dangerous".
Once the notice is served, the dogs must wear a reflective collar at all times and a muzzle and leash in public. There must also be adequate signs at the entrance to the property to warn people there is an aggressive dog inside and the owners' yards must be enclosed to prevent escape.
"This is about the strongest action we can take," Mr Giorgi said.
"If they attack again we will be issuing an order.
"Then we'll make an application to the Magistrate's Court to have the dogs destroyed or they can voluntarily surrender them."
The third bull terrier attacked other dogs while off its leash at a school oval in North Perth, once in late 2011 and again last year.
Its woman owner has co-operated with the council and paid all medical bills of the injured dogs.
"The owner of the two dogs that were attacked basically didn't want . . . the hassle of a court case," Mr Giorgi said. "All they wanted was their dog fixed and all the expenses paid. But we are concerned that the dog is still in the community and we are of the opinion that it will happen again."