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Travel chaos has continued to grip Europe, despite the easing of its aerial lockdown as the Icelandic volcano eruption appeared to wane.Some flights have left Paris, Amsterdam and Frankfurt, but Britain, Germany and Ireland's airspace is still restricted.
And with more than 95,000 flights cancelled in the last week, officials warned it might take weeks to get thousands of stranded passengers home.
The disruption is having an increasing impact on business across the world.
Scientists say southern Iceland's Eyjafjallajokull volcano is producing more lava, and the ash plume was shrinking, although it remains changeable.
Cheers
The Brussels-based Eurocontrol air traffic agency said more than half of Europe's 27,500 daily flights were expected to have flown by the end of Tuesday.
The air traffic agency said it was optimistic the situation would be back to normal in a few days' time.
Weary passengers cheered and clapped as flights began to take off from airports.
"I've never been so happy in my life going back home," a Los Angeles-bound traveller told news agency AFP in Paris. "I love France, but to be going home is something else."
There was more good news for flyers as Air France said it would resume all long-haul flights from Wednesday, although medium-haul flights in northern Europe would stay suspended.
Norway has reopened all of the country's airspace until midnight.
Elsewhere in Scandinavia, airports in north-central Sweden were operating, although Stockholm's main airport was being closed due to the ash cloud.
Warship home
Finland's airspace remained shut while Denmark's was open to long-haul flights.
Several Danish airports, including Copenhagen, were expected to open for six hours on Wednesday morning.
Germany, meanwhile, extended its flight ban to midnight, although 800 flights were allowed to fly visually at lower altitudes.
UK airspace, including all the major airports around London, is expected to remain largely shut until midnight, too.
Nearly 300 lucky British holiday-makers marooned in Santander, northern Spain, were picked up by a Royal Navy warship.
The first five of a fleet of coaches promised by the UK government to help crowds of its nationals home were expected to leave Madrid on Tuesday evening.
All airports in Spain are open and its government has suggested other countries use Madrid as a hub to get passengers moving.
Swiss and northern Italian airspace has reopened, while Turkish airports have also been operating.
In an effort to unblock the travel logjam, EU transport ministers have sought to reduce the size of the no-fly zone.
But Transport Commissioner Siim Kallas denied the EU had taken too long to respond, saying people's lives were at stake.
Business agony
The flight ban was imposed because in the high temperatures of an engine turbine, ash can turn to molten glass and cripple the engine.
As waylaid travellers scrambled for other modes of transport, ferry and railway companies enjoyed an unexpected bonanza, while some car-hire firms were reportedly hiking charges.
But many other businesses have been suffering because of the chaos.
The airline industry says it has been losing more than $200m a day (£130m; 150m euros), since the turmoil began last week.
A shortage of parts has led the car-makers BMW, in Germany, and Nissan, in Japan, to temporarily halt production.
Blocked shipments of goods are reportedly stacking up in China, while South Korea is stuck with hundreds of thousands of mobile phones.
And there are heaps of clothing bound for Europe piling up in Bangladesh.
Meanwhile exporters of fresh flowers and vegetables in Zambia, Kenya and Uganda are having to throw away tonnes of rotting stock.
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