At its Tuesday work session, the council considered whether to fashion a new ordinance that would allow banners equivalent to 25 percent of the outside surface of the library and 60 percent of The Leonardo's wall space.
The banners could go up three weeks before an event and would have to be taken down within one week afterward.
Also according to the proposal, private-sector tenants on the library's ground floor would be able to put up exterior signs no greater than 20 square feet with a maximum height of 14 inches.
Previous City Councils have adopted "sign overlay zones" for EnergySolutions Arena, Spring Mobile Ballpark and areas of the downtown business district that allow huge banners, but commercial signs on city-owned buildings, like the library, is a new issue.
Some on the council embraced the proposal for banners but did not like the signs for shops within the library.
Councilman Luke Garrott said signage for the privately owned shops presented a choice: To maintain a public space that is not "polluted by commercial speech" on one hand. Or to promote the viability of the businesses, on the other.
Council Chairman Soren Simonsen said having numerous signs of private shops on the outside of the library would be troublesome. It would detract from the building and the signs would not be next to the businesses they name on the inside of the building.
But Councilman Carlton Christensen said there should be a sign outside the building near the TRAX station alerting passersby to the specific businesses inside.
The matter has not been scheduled for a vote.