Veterinarian Stephen King expressed concern Tuesday about any new law that would target specific breeds.
Being proposed is an ordinance that would go after pit bulls, Rottweilers and dobermans.
Council President Fred Pitts and Councilman Jonny Davis said any new law needs to include language addressing pit bulls.
Animal control officer Becky Paul told members of the council she believes the proposal needs more work, adding that what's being considered now is less restrictive in some areas than the current law.
There's no indication when the city council will be ready to vote on a tougher ordinance.

The people of this state should not only ban most animals considred pets, the state should also ban all breeding of domesticated animals and people in general. Mississippi is a welfare state and just like every welfare state, should have extreme restrictions on it.
My goldie and I will be content to sit here a thousand miles away (thankfully) as we will never step foot in that joke of a state again. Good day.
So far he has not bitten anyone. It is bad enough that he goes after adults but what could have happened if it was a child walking down the road? An elderly person? Someone walking with a walking stick. This dog goes bonkers when someone picks up a stick.
This dog is a lab. No law should be breed specific. It is the owners that create bad dogs through their abuse, neglect, and inappropriate training. Enforce the laws on the books. If you need to do something, then modify existing law so that aggressive dogs can be picked up when neighbors complains. Fine the owners, and require resocialization of the dog. If people still complain, remove the dog from his home, require the owner to pay for holding the dog until a new home can be found.
People have the right to protect themselves and others from aggressive pets. However, I generally think it should be against the law to kill a pet; any owner who intentionally kills a pet should be given a hefty fine as should anyone who decides he just dislikes an animal and decides to take them out.
It is sheep such as yourself that empower the "good leaders" to rape you to death and you are too passive and complacent to realize it.
You have been successfully victimized and thoroughly pacified. You "love big brother." Your city council are swine. Pig Boy Barbour is swine. Mullet Coif Hood is swine.
If you are terrorized by pit bulls you are an idiot. I love pit bulls. I have been bitten by two dogs in 67 years, a Boston Terrier when I was 9 and a Chihuahua when I was in my 60s. Today I had a Lab mix jump on me, kicked her hard in the guts. She left me alone. I am more afraid of house cats, deers, possums, coons than pit bulls. Get a life. Stop thinking in catch phrases provided you by the likes of Fatsy Scumfield. Grow up, if possible, cultivate an original thought.
Remember that painting of Washington crossing the Delaware? Those guys fought and died for your freedom and you capitulate to scumbags rather than think for yourself and accept the responsibilities of freedom. Shae on you unworthy citizen. Shame.
"Dweeb", you just continue to prove my point. Thank you for persisting to show why Washington crossed that river. I would tell you what a Moron YOU are, but that would be an insult to Morons.
Perhaps you're just angry that people keep pets you don't approve of, but if they're not breaking the law, then you're out of luck. I don't think that people should be able to make laws deciding that people only have the kind of pets that they feel are "appropriate." At the end of the day, once you kowtowed to everyone's opinion, no one would be able to own a dog at all. Half the dogs I've heard people call pit bulls or rottweilers are neither. Ignorance abounds as far as identifying specific breeds of dogs, and when you start legislating against breeds you get a whole lot of misidentification and a lot of family pets off to the slaughter because of it.
Most of the problem with vicious dogs comes from the type of people who wouldn't operate within the law anyway. They wouldn't bother registering the dogs, or insuring them or anything else. They'd simply take their chances until the law came and carted the dog off to be killed.
Alternatively shock collars might work nicely.
What bozos!
If the current leash laws were enforced it would solve 99% of the problem.