Birmingham City Council says it is on track to clear a backlog of uncollected waste by the weekend, despite the ongoing dispute with the Unite union.
Craig Cooper, strategic director of city operations, said collections would focus first on "the poorest parts" of the city "affected the most" by the ongoing bin strike.
Mr Cooper said the amount of uncollected waste had peaked at 22,000 tonnes, but he expected to be back to "one household collection every week" for all residents by the weekend.
Hundreds of bin workers began an all-out strike on 11 March, in a standoff with the Labour-run council that has led to bin bags and fly-tipped rubbish piling up on streets.
The city's residents are caught in the middle of the dispute, and many have told the BBC of their increasing frustrations, with one saying it "can't go on".
Striking workers held a rally on Tuesday morning, a day after Unite union members rejected the city council's latest pay offer.
"We're already back to collecting normal household waste this week," Mr Cooper said. "We are back into a position of good control.
"The priority now is street cleansing and making sure the fly-tipping is at a manageable level."
He added that the council had 120 bin lorries out every day completing rounds, which was roughly half of its total capacity.
Garden waste and recycling will not be collected by the authority until the strike is over, he said.
Mr Cooper described it as "disappointing" that an agreement had not been reached with Unite and urged them to "come back to the table" to end the dispute.
More negotiations between the two sides are expected to take place on Wednesday.
