The Zoning Board of Appeal on Tuesday rejected a proposal to couple the erection of a digital billboard in the backyard of the Polish-American Citizens Club on Boston Street, overlooking the Expressway, with the elimination of three existing billboards elsewhere in Dorchester.

Polish-American officials and supporters said the rental revenue from the proposed bill would help keep the group afloat - and would result in a net reduction in the number of billboards in the neighborhood. But the BPDA opposed the proposal because the city has long opposed all new billboards. In fact, the proposal needed zoning variances because city zoning code prohibits new billboards.

At least three of the board's seven members - Eric Robinson, Jeanne Pinado and Chairwoman Christine Araujo - voted against the proposal, which means it was defeated because state law requires at least five yes votes. One member, Mark Erlich, raised a question during voting but did not appear to vote either for or against, but it wouldn't have mattered even if he did vote yes because that still would have left the proposal one vote short.

Billboard company Media Partners had proposed erecting a pylon in the club backyard, right over I-93, topped with a 14x48 electronic billboard, designed with technology to minimize the light shining on nearby properties.

As part of the proposal, the company said it would agree to a condition that a permit for the billboard not be issued until after it had worked with the owners of three other billboards in Dorchester to take their signs down. One would actually be two two-sided billboards at Dorchester Avenue and Freeport Street, the company's attorney, Ryan Spitz said. He said the other two locations would be determined through consultation with City Councilor Frank Baker and the McCormack Civic Association - and then negotiations with the owners and landlords of the other locations.

"I don't think I've ever heard anything like that before," Erlich said. Spitz said such arrangements have worked in other areas.

Elizabeth Scibeck, who lives right next to the club, on Rawson Street, supported the proposal. She said she's Polish, she grew up in the Polish Triangle and she realizes that the rent from the billboard would help keep the club open. "It's an important organization in the community," she said.

"This billboard would sustain the future of this club," agreed nearby resident Erica Manczuk Stocks.

Also supporting the proposal: At-large City Councilor Michael Flaherty. His aide, Paul Sullivan, told the board the plan would remove some blight in the rest of the neighborhood and would help ensure a long-time non-profit group would stay in existence. The McCormack Civic Association also voted to approve the idea, although the neighboring Columbia-Savin Hill Civic Association opposed the proposal.

Jeff Hampton, the BPDA's zoning director, called the site "an inappropriate location" for a billboard. Then again, the BPDA has long opposed new billboards anywhere in Boston.

Some board members, including Erlich, expressed concern that the formal proposal before them did not include renderings of the proposed billboard. "We kind of know what a billboard looks like," board Chairwoman Christine Araujo said after Erlich raised the issue after member Joe Ruggiero moved to approve the project - subject to three other billboards coming down first.