City officials Tuesday night unveiled a proposal for a “single-stream” system that also would make many items now destined for the trash container — cereal boxes, junk mail and aluminum foil — eligible for recycling.

The council is set to vote July 28 whether to accept a bid from Westbury-based Winter Bros. Waste Systems to handle the program. If approved, single stream is set to begin in Glen Cove on Aug. 3.

“It makes us cleaner, greener, leaner,” Mayor Reginald Spinello said of the program.

“Leaner” referred to how the city would save more than $70 a ton when it recycles material that residents now throw in the garbage can, officials said.

Winter Bros. would pay the city $5.05 per ton of recyclable material, city public works director James Byrne said. In addition, the city would save about $65 a ton in disposal costs. Each 10 percent increase in recyclable material collected would mean $90,000 in savings for the city, he said.

Glen Cove officials said Tuesday that they were introducing Nassau County’s first single-stream program, but the city of Long Beach and the village of Lynbrook introduced all-in-one recycling earlier this year.

In Long Beach, the amount of recyclable material collected under single stream soared more than 53 percent in January through March of this year — the first three months of the program — compared with the same period last year, city spokesman Gordon Tepper said.

In Suffolk County, the Town of Brookhaven saw its collection of recyclables rise by nearly 24 percent in one year after it began single-stream recycling in January 2014, Town Supervisor Edward P. Romaine said.

“It caught fire because it was far more convenient” for residents, he said, adding that the program saved the town about $450,000 last year.

Brookhaven also contracts with several towns and villages in Suffolk County to handle single-stream recycling through its Yaphank facility, which is leased by Green Stream, a company co-owned by Winter Bros.

Single-stream recycling has been around for years, but it has become increasingly popular as the technology for separating different types of recyclables has improved, said Brenda Pulley, senior vice president for recycling for Stamford, Connecticut-based Keep America Beautiful, a nonprofit that promotes recycling.

Most U.S. communities beginning curbside recycling now start with single-stream, and many places with existing recycling programs are switching to it, she said.

Currently in Glen Cove, residents must put bottles, cans and plastic beverage bottles in a blue recycling container. They then have to bundle up newspapers and magazines and set them out separately. Corrugated cardboard also must be separated and is typically picked up on a separate day.

“It’s very cumbersome,” Byrne said of the outgoing system.