Cardiff and the Vale, Abertawe Bro Morgannwg and Hywel Dda health boards now face what is known as "targeted intervention".
It is the second-highest of four levels of oversight.
This is one level below being put in special measures.
This already applies to Wales' largest health board, Betsi Cadwaladr in north Wales, which was taken under direct control in June 2015.
All three health boards, according to Health Secretary Vaughan Gething, were unable to set out convincing medium-term plans to deal with local challenges.
The organisations are being monitored against a one-year improvement plan.
The decision, announced in a written statement to AMs, follows a twice-yearly meeting between the Welsh Government, Wales Audit Office and Healthcare Inspectorate Wales.
Meanwhile the Welsh Ambulance Service's escalation level has been downgraded to the lowest level of oversight - following what the Welsh Government describes as "considerable progress" made by the trust.
All other health organisations in Wales remain at their previous "escalation levels."
According to Mr Gething, Abertawe Bro Morgannwg - which is responsible for hospitals in Swansea, Neath Port Talbot and Bridgend -  in addition to not having an approved three year plan,  faced "continuing challenges in respect to unscheduled care and cancer."
The health board said it had made "significant progress" and made improvements in many areas "but recognise that we are currently facing a number of specific challenges about how to best deliver sustainable services that meet the increasing needs of our population".
Although Cardiff and Vale health board's performance recently improved in "key areas" - the health secretary said it "did not provide me with the necessary confidence that the organisation has a deliverable and affordable plan for the next three years."
Meanwhile Hywel Dda "faces a number of long-standing challenges" - which needs a "strategic solution" to make sure its services are sustainable"
There are four levels of escalation in the Welsh NHS which reflect increasing levels of concern:
Three health boards in Wales have been placed under an increased level of scrutiny and control by the Welsh Government due to doubts about their ability to tackle their challenges.