Swansea Council is hopeful that it will meet an important target at the end of March and avoid costly fines.
Every council in Wales needs to reach a recycling rate of 58% for 2016. The target is set by the Welsh Government and failure to meet the rate could mean heavy fines are handed out.
Last year the council's annual rate was just over 56% and was boosted by the introduction of a three bag limit to black bag waste collections.
David Hopkins, Cabinet Member for the Environment and Transportation, said, "The indication is that we will achieve the 58% target.
"My hope is that we can continue to encourage more households to recycle and our percentage continues to increase.
"We simply cannot continue disposing of thousands of tonnes of black bag waste in landfill when we know that much of it can be recycled.
"It costs the council around £4 million a year in landfill costs."
The council recently carried out a survey of household waste in low performing areas including some streets in Townhill where residents are putting out more than three black bags.
A search of the abandoned black bags showed that more than three quarters of the waste was recyclable material.
Cllr Hopkins added, "We have more work to do to get households on board that do not recycle.
"Our kerbside collections provide a wide range of opportunities for residents to responsibly get rid of almost all their household waste by recycling it.
"We know that those that are recycling are staying well within the current three bag limit."