Little pups that want to run with the big dogs will have to stay out of downtown Winslow and Lynwood.

The Bainbridge Island City Council has agreed to change its animal control ordinance to require dogs to be on leashes in the Winslow area and in the Lynwood Neighborhood Center.

Off-leash dogs are already prohibited in Bainbridge parks — with the exception of park-approved off-leash areas — and on school district property. At the council’s meeting Tuesday, council members agreed to revise the rules, but also decided to keep the current restrictions in place for other parts of the island.

Outside the Winslow area and Lynwood, dogs don’t need to be on leashes but must be under the control of their owner’s voice.

The council has grappled with changes to its animal control ordinance for months. At earlier meetings, dog owners have packed council chambers at city hall and have lobbied the council to continue to allow off-leash dogs on Bainbridge.

Other residents, however, have supported a stronger leash law and shared stories of dog attacks and other out-of-control animals.

Under the new rules — which are set to be adopted at the council’s meeting on March 24 — the Winslow area where dogs must be leashed extends from Eagle Harbor north to High School Road, and from Madison Avenue on the west to Ferncliff Avenue on the east.

Council members said the new rules were not a drastic change from what’s already on the books. Loose dogs are currently not allowed in most public parks.

And Councilman Wayne Roth said virtually every dog he sees in town is already on a leash.

“It isn’t as if there’s a great change of habit that’s going to happen,” Roth said.

“There isn’t a radical change here,” he said.

Council members considered several final tweaks to the revised rules.

Recalling a comment from an islander earlier in the day, Mayor Anne Blair asked if the leash law that covers the Winslow area should be expanded to the south to other high density areas.

Councilman Val Tollefson, however, said the boundary set for Winslow was meant to be easy to understand for residents and dog owners.

He also noted that many of the concerns raised by residents on both sides of the issue were centered on off-leash dogs in parks.

Tollefson suggested that the city use Pritchard Park, which is city property that is slated to be turned over to the Bainbridge park district later this year, as a test case and allow dogs off-leash but under their owners’ command during specific days.

The city would then “be able to demonstrate during that trial period to the park district that this really does work, and that owners can self-police themselves and other dog owners,” Tollefson said.

The changes were approved on a 5-2 vote.

Blair and Councilman Michael Scott voted in the minority.

“I’m going to vote against this, fully knowing it’s going to pass,” Blair said.

She said the voices of those who wanted an island-wide leash law “need to be respected.”

“I very, very much appreciate the compromise of this, and I realize it’s not satisfying to anyone,” Blair added.

Scott said he voted no because he favored an all-island leash law for city streets and rights-of-way.

Council members agreed to put the revised changes on the next council agenda for final approval.