Harrogate Borough Council is testing out the blue-lidded bins as a replacement for black boxes which residents complain are not big enough and result in recycling being blown across streets during bad weather.
The Appleby estate in Knaresborough was chosen as the first area for the trial and now more locations have been revealed.
Councillor Sam Gibbs, cabinet member for environment, waste reduction and recycling at the council, said around 2,000 bins have already been rolled out and that 880 more in Bilton and 1,800 in Ripon will follow this month.
He also said 2,000 will be introduced in the Harlow Hill and Arthurs Avenue areas of Harrogate in August.
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When questioned how the trial is going, councillor Gibbs told a council meeting that residents seemed "very happy" with the changes, although there had been some issues with items including a bouncy castle and petrol cans being incorrectly placed in the bins.
Councillor Gibbs said: "One thing we pride ourselves on as a council is the low contamination rates of our recycling which has enabled us to recoup as much money as possible.
"Whether this trial is a success or not will depend on the cleanliness and contamination rates of the recycling that we collect.
"So far, albeit from a very small sample size, things are looking good."
Recycling that contains contamination - including the wrong items or food waste - costs more to dispose of and the recycled material produced can be of lower quality.
The new wheelie bins can be used to recycle glass bottles, jars, tin cans, foil, food and drink cartons, and plastic bottles and tubs.
Blue bags for recycling paper, card and cardboard will continue to be used.
However, these will be replaced with heavy-duty bags for those properties that don't have them.
By Jacob Webster, Local Democracy Reporter