The Zoning Board of Appeal on Tuesday approved a new three deckers on what are now vacant lots on Church Street at Fifield Street and Fowler Street, but rejected one proposed to go behind an existing three decker on Homes Avenue.

The board unanimously approved a proposal by Sean George and Scott Kirkwood for a new three decker on a roughly 2,660-square-foot lot 16 Church St., where a three decker stood until the 1970s.

The new building, which their attorney, Ryan Spitz, called "a traditional-style three-family dwelling," would have two parking spaces off Fifield Street.

Board member Eric Robinson said the new structure, which required several variances, was consistent with other buildings in the area.

The board approved the proposal subject to review by BPDA designers; Robinson said he hoped that would include reducing the width of the curb cut for the parking spaces from 18 feet to something more pedestrian friendly. Typical driveway widths tend to be 10 or 12 feet.

City Councilors Frank Baker and Michael Flaherty supported the proposal.

Also winning board approval: A new three decker proposed by Neil Gulden at 15 Fowler St. on a roughly 4,200-square-foot lot.

Flaherty supported the proposal as well.

The board, however, rejected a proposal to build a three decker at 118R Homes Ave., behind 118 Homes Ave., saying its unusual location meant it did not deserve variances on a lot that was already too small for the two-family house it was zoned for.

Owner Anthony Monahan of Quincy said he wanted to do something with the roughly 4,500-square-foot landlocked lot, which, however, has an easement for the driveway that enters from Homes Avenue. At the request of the local neighborhood group, his plans showed six parking spaces.

Monahan said the neighborhood had some similar landlocked rear lots, but acknowledged that none had more than a two-family house on it.

A couple living next to Monahan's property opposed the proposal. "There's not enough space, there's not enough room," Susan McKenzie said.

A three-story, three-unit building for the relatively small lot zoned for a two-family house surrounded by other lots "seems excessive," board member Mark Erlich said.

The Boston Transportation Department proposed eliminating two of the parking spaces, saying otherwise there would not be enough room for maneuvering cars in and out of the spaces.

The board rejected the proposal without prejudice, which means Monahan could come back within the year with a proposal for a one- or two-family building.