A bed was among rubbish dumped at the Annagh on Sunday - just the day after 15 tonnes of rubbish was collected as part of a major cleaning blitz by the council.
A councillor has warned that “patience is wearing thin” and the council may be forced to take a harder line if the situation does not improve.
The one-off, amnesty clean-up was organised by ABC Council following complaints from residents.
Skips were placed in Queen Street/ Cecil Street, and Burnbrae Avenue and Queen Street, with staff working for up to six hours to clear rubbish.
Alderman Robert Smith said, “Landlords need to step up to the mark and make sure their tenants are responsible for their actions.
“There have been a number of meetings with council officials and landlords and ultimately the responsibility lies with landlords and tenants.
“If rubbish is dumped in an alleyway behind the houses, then there should be some sort of collective response from landlords.
“Now the area is cleaned up, this is a good chance for them to get on top of it.”
Alderman Smith said there had been leaflet drops in the area to educate and inform tenants.
A regular handcart cleanup service has also been introduced in the Annagh, as well as Rectory, Brownstown and Corcrain.
He appealed to anyone who witnessed dumping in the area to phone the DUP office on 3833 2234 or the council’s environmental services department on 3831 2400.
Under the law, the council can fine anyone found guilty of littering or fly-tipping.
Meanwhile, the next meeting of the Annagh Residents’ Forum has been rescheduled. It will now take place on Wednesday, November 2 at Presentation Primary School.