All adults living in Cardiff and the Vale of Glamorgan can now join a reserve list for a first dose of coronavirus vaccine.
Cardiff and Vale University Health Board confirmed on Wednesday that their online reserve list is now available to anyone over the age of 18.
A spokeswoman said people will be allocated an appointment in chronological order and will be called to attend a vaccination centre at short notice.
"The health board is committed to vaccinating the population of Cardiff and the Vale of Glamorgan as quickly as possible," the spokeswoman said.
"We have vaccinated the priority group 1-9 ahead of the April 19 target and have this week been moving through the 40-49 age cohort. More than half (51%) of this group has now been vaccinated and all have been scheduled appointments so we are now able to invite people in their 30s.
"We have a reserve list in place to ensure there is no vaccine wastage and anyone over the age of 18 can join the reserve list by completing a form on our website.
"Once details are entered individuals will be contacted in chronological order - oldest first when an appointment is available. Please note this will require individuals to be available to attend at short notice."
For all those in priority groups 1-9 who have not yet received their vaccination, the health board has created a 'Leave Nobody Behind' form.
The spokeswoman added: "The form is available on our website and once completed, individuals will be contacted and prioritised for a vaccination appointment. The oldest people on the reserve list will be offered appointments first but our leave nobody behind list will take priority."
Both of these forms can be found on the Covid-19 Mass Vaccination Programme section of the health board's website here.
We went to the community vaccination centre in Splott in early March as the rollout was gathering pace
"We do not advise people turning up at any of our sites without an appointment as this adds additional pressure to the service and our staff," the spokeswoman added.
"Please look out for official updates on our website and social media channels where we will keep people updated with when they will be called."
Fiona Kinghorn, the executive director for public health at Cardiff and Vale UHB, said she was concerned about a rise in people not turning up for their appointments.
She said an average of 8% of people were no-shows and there are felt to be a number of reasons why.
Ms Kinghorn told BBC Radio Wales on Wednesday: "We are finding that a percentage of people as we move down the age cohorts, we are having some did not attends. In part, we think that is because we don't always have the right details for people.
"We have got an average of about 8% no shows. If we were giving 4,000 vaccines in a day, about 8% as we move down the age cohorts did not show.
"We think there is a mixed set of reasons. It might be that someone doesn't want the vaccine, it might be that the details are slightly wrong. That is why we are trying different ways of getting people in.
"We are saying if you are 40 and over, please ring our booking line and if you are under 40 we have a reserve form you can fill in.
"It is just a belt and braces approach to complement our auto-scheduling system to make sure everyone has the offer and make the decision to have the vaccine.
"The no show percentage is higher than it was and it is interesting that we are seeing it as we move down the age groups. Older age groups might have been particularly keen to get the vaccine.
"It is a concern for us, and my key message is 'please get your vaccine' when you are offered. It is one of our key lines of defence."
She added that the risk of Covid-19 "far outweighed" the risks of blood clots from any vaccines.
The latest figures also show that 1,621,282 people have received the first dose of a Covid-19 vaccine and 549,193 people have had both doses. Earlier this week Wales became the first UK nation to give a first dose of a vaccine to more than half its population.
