"Everyone was screaming in the airplane from happiness," said Savvas Toumarides of Cyprus, who arrived in New York after getting stuck in Amsterdam for five days and missing his sister's wedding. He said the worst part was "waiting and waiting and not knowing."
"We were in the hotel having breakfast, and we heard an aircraft take off. Everybody got up and applauded," said Bob Basso of San Diego, who has been stranded near Charles de Gaulle since Friday.
The Eurocontrol air traffic agency in Brussels said it expected just under half of Europe's 27,500 flights to go ahead Tuesday, a marked improvement over the last few days. The agency predicted close to normal takeoffs by Friday.
"The situation today is much improved," said Brian Flynn, deputy head of operations at the Brussels-based agency.
But with more than 95,000 flights canceled in the last week alone, airlines faced the enormous task of working through the backlog to get passengers where they want to go -- a challenge that could take days or even weeks.
Passengers with current tickets were being given priority -- stranded passengers were being told to either pay for a new ticket, take the first available flight or to use their old ticket and wait for days, or weeks, for the first available seat.
"I'm supposed to be home, my children are supposed to be in school," said Belgian Marie-Laurence Gregoire, 41, who was traveling in Japan with her husband and three children, ages 6, 8, 10. They said the best that British Airways could do was put them on a flight to Rome.
"I'm tired. I just want to go home," she said.
Although seismic activity at the volcano has increased, the ash plume appeared to be shrinking Tuesday. Still, scientists were worried that the activity could trigger an even larger eruption at the nearby Katla volcano, which sits on the massive Myrdalsjokull icecap and has erupted every 80 years or so -- the last time in 1918.
"The activity of one volcano sometimes triggers the next one, and Katla has been active together with Eyjafjallajokull in the past," said Pall Einarsson, professor of geophysics at the Institute of Earth Sciences at the University of Iceland.
At eruption at Katla could spark similar travel disruptions, depending on the prevailing winds. But in Iceland's eight volcanic eruptions in the last 40 years, only the recent one at Eyjafjallajokull was followed by winds blowing toward northern Europe.
An international pilots group warned of continued danger because of the ash, which drifted over the North Sea and was being pushed back over Britain on Tuesday by shifting north winds.
A Eurocontrol volcanic ash map on Tuesday listed the airspace between Iceland, Britain and Ireland as a no-fly zone, along with much of the area around the Baltic Sea. The ash cloud also spread westward from Iceland, toward Greenland and Canada's eastern coastline.
Still, planes were being allowed to fly above 20,000 feet (7,000 kilometers) over the United Kingdom.
Herbert Puempel at the World Meteorological Organization in Geneva said there was a small possibility that some far-flung airports on the Canadian east coast, such as Goose Bay or Thunder Bay, might be affected by the ash but said "a serious effect on the eastern seaboard I think is very unlikely."
The volcano was also grumbling -- tremors, which geologists believe to be caused by magma rising through the crust, can be heard and felt as far as 16 miles (25 kilometers) from the crater.
"It's like a shaking in the belly. People in the area are disturbed by this," said Kristin Vogfjord, geologist at the Icelandic Met Office.
Scottish airports let in a handful of domestic flights, while Switzerland and northern Italy also opened their airspace. Some flights took off from Asia to southern Europe and came in from Cairo, where at least 17,000 people had been stranded.