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.