People aged in their 40s will be next in line to get the coronavirus vaccine, Wales' chief medical officer has said.
The four UK nations are doing this, under the plan to vaccinate all adults by the end of July.
Dr Frank Atherton said the plan for Wales depends on "supply matching our ambition".
Teachers and police officers were among those who lobbied to be prioritised - but will now be vaccinated in line with their age group.
News of the next phase comes as Public Health Wales figures show more than 270,000 people aged in their 50s and 60s, have had their first dose of Covid vaccine.
All four of Wales' chief constables have criticised the decision not to prioritise frontline workers, saying they were "incredibly disappointed".
Head teachers' union NAHT Cymru said all front-line staff "should be protected now".
Speaking at the Welsh Government's coronavirus briefing, Dr Atherton said there was not enough evidence to support prioritising people from specific occupations in the next phase of the vaccine rollout, as outlined by the Joint Committee on Vaccination and Immunisation (JCVI).
"I, along with the UK's other three chief medical officers support the JCVI advice and the four UK governments have agreed to implement it," he said.
"This means the UK's vaccine programmes remains aligned as we all work towards one shared goal.
"This is the simplest, quickest and fairest approach. And it means we can remain on track to meet our ambitious vaccination targets."
He said calls for people in specific occupations to be prioritised had been heard.
"The JCVI did consider this - however, it found there wasn't sufficient evidence to set specific occupations apart from the general population. It also advised that the complexity of delivering this approach would slow down the pace of the vaccination roll-out," he added.
However Laura Doel, director of NAHT Cymru, said that despite such complexity it was "not a good enough reason not to prioritise the needs of committed professionals".
"We call upon the Welsh Government to take a different view… front line staff should be protected now that those in the greatest danger have already been vaccinated," she said.
"They are being required to work with large groups of people who carry at least as much potential for infection as anyone else.
"Those groups often occupy confined and unventilated spaces for long periods of time with only rudimentary PPE."
In a joint statement, Wales' four chief constables - Carl Foulkes of North Wales Police, Mark Collins of Dyfed Powys Police, Pam Kelly of Gwent Police and Jeremy Vaughan of South Wales Police - said: "We have repeatedly asked that policing be risk assessed so our officers and staff can be given due consideration, given the risks they take daily on behalf of us all.
Disappointed isn't the word.Last night officers attended a call where a person was violent-difficult for hospital/ambulance staff to manage.Officers controlled the situation.soon confirmed that the person had COVID.Officers are now isolating. No vaccine for police=unfair https://t.co/vQoahdJpdw— Chief Constable Pam Kelly (@GP_CCKelly) February 26, 2021
"Police officers by the nature of their role have to go into different settings and come into contact with all high risk groups along with also being unable to social distance and on many occasions cannot maintain PPE as designed, given the physical role they have to undertake," they wrote.
"In addition they are being tasked with enforcing isolation and quarantine arrangements on the government's behalf on those they know have the virus."
'Concerns over supply'
The total number of people to have received their first dose of a Covid vaccine in Wales is 902,334 and 80,062 of those have had their second dose.
In a statement, Health Minister Vaughan Gething said: "It is encouraging that the UK Government has brought forward some of Wales' supply allocation.
"But from the information available to us at this point there are concerns with both the type of supply and the timing of its delivery.
"We have always said that we could go even faster were the supply available."