The quality of children's services in Darlington has improved since a damning report in 2015, but more still needs to be done, government inspectors say.
Ofsted rated services as inadequate in September 2015, blaming "serious shortfalls" in management.
But despite improvements some children at risk are still not being dealt with effectively enough, inspectors said.
The Labour-run council said it was pleased its "considerable achievement" had been recognised.
In the last inspection, Ofsted said there were unchecked "serious failures by senior leaders... to take oversight of, and accountability for services."
Almost three years on and inspectors said "leadership and governance" had markedly improved, rating services as "requiring improvement to be good".
But they said while no children were found to be in situations of "unassessed or unmanaged risk", some suffered too many placement moves.
It also said the matching of children with foster carers and the training of and information sharing with the carers was not sufficiently developed.
The health needs of looked after children were also not being consistently assessed or reviewed in a timely way, the latest report says.
The quality of the adoption service remains good, but alternative permanent options for children are "not pursued as effectively".
Suzanne Joyner, Darlington's director of children's and adult services, said: "It's very pleasing that Ofsted has recognised the progress and improvements that have been made since 2015.
"We cannot and will not rest on our laurels, our improvement journey will continue, we aim to be graded good in the future."