The Walsh administration is expected to file a petition Monday to boost the chances of a 775-foot tower getting built in downtown Boston at the expense of future skyscrapers.

A Millennium Partners proposal to build a mixed-use tower at the site of a vacant, city-owned parking garage in Winthrop Square has been met with resistance due to the amount of shadow it would cast on the Boston Public Garden and Boston Common. Tantalized by the $153M the city would receive from the 115 Winthrop Square sale, the Walsh administration is proposing a compromise to local park preservationists: permit the tower but limit further tall development around the city’s green spaces, the Boston Globe reports.

Mayor Marty Walsh’s proposal would bar future developments (except Millennium’s) from casting a shadow over the Common, Public Garden and Back Bay’s Copley Square. The plan would also call for new zoning in the Financial District and Downtown Crossing. The shadow change also needs state approval by Gov. Charlie Baker and the state legislature due to the changes it would bring to the Massachusetts' 1990 shadow law.

The Winthrop Square development has already drawn criticism from the Massachusetts Port Authority, Logan Airport’s operator. The skyscraper would hamper operations at the airport, as anything taller than 710 feet would block a heavily utilized takeoff corridor, Massport said. Similar concerns regarding the airport previously halted the late Mayor Thomas Menino and businessman Steve Belkin’s push for a 1,000-foot tower on the Winthrop Square site in 2008.

While the city has promised funds from the sale would go to Boston Common, Franklin Park in Jamaica Plain and for public housing renovations in East Boston and South Boston, a shorter tower would mean less money for Boston. The city said it will receive the $153M sum from the garage sale, but $51M of the deal is tied to condo sales. Lopping off a few floors to appease the FAA and Massport would mean fewer condo commissions for the promised sale figure.