On a 10-0 vote, the council declined to grant historic-cultural monument status to the downtown structure that once served as the
The vote comes as council members consider a separate plan to knock down the 1955 building to make way for new offices for city workers.
Preservationists are pushing to save Parker Center, which is best known for appearing in the TV series "Dragnet" and named for controversial former Police Chief William Parker.
The structure is one of many buildings in the Los Angeles area designed by Becket, who established his architecture firm in the city in 1933. His work includes the Capitol Records Building, the Santa Monica Civic Auditorium, UCLA's Pauley Pavilion, the Cinerama Dome and the jet-age Theme Building at Los Angeles International Airport.
The Los Angeles Conservancy calls the eight-story Parker Center a "significant postwar addition" and wants City Hall to incorporate it into the new office structure.
But a city engineering report presented to council members last month recommends against adaptive reuse, stating that it would be more expensive given the structure's poor condition.
Several Little Tokyo groups also support a new building on the downtown parcel, which abuts their neighborhood.
Historical-cultural monument status would have slowed the process of demolition, but not necessarily saved the structure.
Parker's complicated legacy apparently came into play for some council members. The chief, who headed the LAPD from 1950 to 1966, is blamed for widening tensions between police and minority communities.
City Councilman Marqueece Harris-Dawson explained on Twitter last week why he couldn't support the designation. "We can't honor a man who demeaned and derided black and brown lives," Harris-Dawson wrote.
Adrian Scott Fine, the Los Angeles Conservancy's director of advocacy, said in an interview last year that it's important for L.A. to "own its past" rather than wipe it away.