The Dumfries and Galloway authority switched from a single bin to a multi-bin system in Wigtownshire last year.
In April it was flagged up that the costs had proved much higher than initially anticipated.
However, an exact figure will not be put on that increase until later this year.
A council statement said: "The household waste and recycling collection service in the Wigtown area is a new service and both the operations and financial costs are under review.
"The outcome of this review will be first presented to members in autumn.
"The review process will help inform the future schemes to be rolled out over the rest of Dumfries and Galloway."
Dumfries and Galloway Council used to run a single wheelie-bin system thanks to an Eco Deco plant which separated waste so householders did not have to.
New regulations prompted the council to move to the multi-bin system with five new recycling containers issued.
A council has said the scale of a "significant increase" in the cost of a new multi-bin waste collection system will not be revealed until the autumn.