The world's net rate of forest loss has slowed markedly in the last decade, with less logging in the Amazon and China planting trees on a grand scale.
Yet forests continue to be lost at "an alarming rate" in some countries, according to the UN Food and Agriculture Organization (FAO).
Its Global Forest Resources Assessment 2010 finds the loss of tree cover is most acute in Africa and South America.
But Australia also suffered huge losses because of the recent drought.
"It is good news," said the report's co-ordinator Mette Loyche Wilkie, a senior forestry office with FAO.
"This is the first time we've been able to say that the deforestation rate is going down across the world, and certainly when you look at the net rate that is certainly down.
"But the situation in some countries is still alarming," she told BBC News.
The last decade saw forests being lost or converted at a rate of 13 million hectares per year, compared to 16 million hectares in the 1990s.
However, new forests were being planted to the tune of more than seven million hectares per year; so the net rate of loss since the year 2000 has been 5.2 million hectares per year, compared to 8.3 million in the 1990s.
Globally, forests now cover about 31% of the Earth's land surface. ...