People will be able to exercise outside more than once a day in Wales, with some libraries, recycling centres and garden centres set to re-open too, First Minister Mark Drakeford has said.
But Mr Drakeford warned it was “too soon” to make any other changes.
The rest of the coronavirus stay-at-home restrictions will be extended for another three weeks.
It comes 48 hours before Prime Minister Boris Johnson announces possible changes to the rules in England.
The changes to the seven-week old lockdown come into force across Wales from Monday.
“We must not lose the progress we have made,” Mr Drakeford said.
“All of us must continue to work from home wherever they can. All of us must only travel when absolutely necessary.”
Despite reports of tensions between the different governments, Mr Drakeford said he wanted to “move in step with the other nations of the United Kingdom”.
He said just a small increase in the rate of transmission of the coronavirus – the so-called ‘R’ number – would mean thousands more in hospital and as many as 7,200 deaths.
Mr Drakeford said as a result of the three-week review, the Welsh Government believed small changes to the regulations could be made.
From Monday people will be allowed to exercise more than once a day, but not to travel “a significant distance” from home.
Garden centres will be allowed to re-open, provided they can ensure the two metre social distancing rule is followed.
And councils will begin to work on plans to re-open libraries and waste centres.
The 120,000 people in the most at-risk groups, who have received official “shielding” letters, should continue to follow that advice.
Mr Drakeford said the R number currently sits at around 0.8 in Wales. Welsh Government estimates suggest that, at that level, 800 may die from coronavirus between 8 May and 7 August.
But he warned that if this rose to just 1.1, “we would see 7,200”.