Small restaurants outside the downtown area could soon start seating patrons who’ve brought along their own six-packs and bottles of wine.

Boston’s City Council moved one step closer to legalizing BYOB in the Hub, facing some pushback but no firm opposition to the idea in a Monday hearing at City Hall.

Supporters say it would be a boon for the underdogs in Boston’s booming dining-out scene: tiny restaurants in outlying neighborhoods without the capital or fridge space to buy pricey liquor licenses and stock up on alcohol.

“We’re looking to bring some of the vitality of our awesome restaurant scene into every neighborhood in Boston and do it in a way that puts public safety front and center,” said Councilor Michelle Wu, who co-sponsoring the ordinance along with her colleague Stephen Murphy.

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The ordinance would allow eateries to get permits to offer BYOB only if they do not already have a liquor license, if they have a wait staff (so no lunch counters or fast-food joints) and are small (no more than 30 seats). It would also require that the restaurants buy liability insurance and that servers take alcohol training courses.

Neighborhoods in city core – for example the North End and Beacon Hill – would not be eligible.

Specific regulations would be up to the city’s licensing board.

Wu said she anticipated permits would cost around $300. That’s far shy of the going rate for alcohol licenses, which start at $3,000 and can fetch as much as $400,000 on a competitive open market.

No outright opponents came to Monday’s meeting. But at least one Boston restaurant lawyer told Metro he was opposed to the idea and called on the city to licensing the way it is.

“Allowing this sort of activity to compete against people who have purchased their licenses seems to be an erosion of a well-set-up and well-functioning regulatory scheme,” said John Connell, who has represented restaurants, alcohol producers and distributors.

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City Councilor Ayanna Pressley, meanwhile, argued instead for more liquor licenses in the city for outlying neighborhoods, without needing the blessing of the Legislature. She led the charge last year that led to 60 licenses being earmarked for seven neighborhoods, among them Mattapan and Hyde Park.

“We just need more licenses,” Pressley said at the hearing. “That still needs to be the greater goal of reform pursued here, which is local control.”

Progress on that front may be stalling: also on Monday, Gov. Charlie Baker announced legislation that would give more control over liquor licenses to cities and towns – except the city of Boston, according to the State House News Service.

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