The wedding bells and cash register may be ringing a lot less at Boston City Hall.

Several Boston city councilors voiced support today for a proposed ordinance that would limit how much outside money the city clerk could make from performing weddings. Under existing law, the clerk can pocket all the money she makes from marrying people on city time and on City Hall property.

Councilor Ayanna Pressley called the current law “a relic from a different era. We can’t allow revenue to be siphoned away.”

Councilor Tito Jackson called the current law antiquated and said the proposed ordinance “epitomizes good government.” A number of other councilors also stood up to speak in support of the proposed ordinance.

The proposed ordinance, filed by Council President Stephen Murphy and Councilor Michael Ross, would require that wedding fees go into the city’s general fund if the clerk marries people during normal business hours. But if the marriage knot is tied before 9 a.m. or after 5 p.m., or during the lunch hour, the clerk could keep the money even though the marriage is being done on city property.

The current clerk, Rosario Salerno, rakes in an estimated $70,000 a year as a justice of the peace performing weddings at City Hall.  The wedding money is in addition to the $102,000 she pulls down as clerk.

The council, facing heat for trying to place one of its former colleagues, Maureen Feeney, in the city clerk’s post, unanimously voted today to hold a public hearing on the proposed ordinance. Salerno plans to retire early next year and the council has made little secret of the fact that it plans to appoint Feeney as her replacement. Feeney stepped down from the council recently, without telling her constituents, so she could be appointed to the clerk’s post by the council.