But they still keep coming -- at an average rate of 1,800 people each day during February.
After hours slicing though dark seas on vessels shared with tourists, refugees often arrive at Piraeus Port in Athens, carrying bundles of blankets, rolled-up tents and babies in their arms.
They dream of making the route through Greece to Macedonia and, eventually, to perceived safe havens like Germany and Sweden.
But since Macedonia started restricting refugee access
-- only allowing a few dozen Syrians and Iraqis across the border each day -- a backlog has built up in Greece.
About 35,000 migrants are currently stranded in the country, fueling fears that Greece is turning into a giant refugee camp -- or "warehouse of souls," as the country's Prime Minister Alexis Tsipras called it.
Some make it to the Greece-Macedonia border...
Thousands -- men, women and children -- are stuck in filthy conditions near Idomeni, a small village in northern Greece. There they are butted up against Macedonia's new razor-wire security fence.
Litter covers the ground, some of it floating in large dank puddles. Food and hygiene facilities are inadequate. All the while, Macedonian guards with assault rifles patrol up and down the border.
But some don't make it that far...
Many refugees don't reach the border -- and if they do, they are bused back to Athens.
Across the Greek capital, refugee tents, lines of drying washing and clusters of homeless people have been springing up in unexpected places.
The United Nations Refugee Agency has filled a baseball stadium, built for the 2004 Olympic Games, with white tents. It's an ironic legacy for the sporting event, which cost vast sums of money: many of the facilities have been quietly falling into disrepair since the world famous athletes departed.
The Olympic hockey stadium has also been given a new, unexpected, lease of life as a temporary home for 3,000 refugees. Today, the bright fabrics adorning the stadium stands are not team banners but the clothes and washing of families from Afghanistan and elsewhere, drying under the Athenian sun.
Inside, families try to create a little privacy for themselves -- and their many young children -- by hanging up pieces of fabric. But supplies are low: just gray United Nations blankets, thin padded sleeping mats, a few toys. There's the occasional cot, but no bed in sight.
Mustafa Saidi from Kabul, Afghanistan, is living here with his wife and daughters, aged three and nine years old.
It took them a month to reach Greece, smuggled in by car and boat: "It was so dangerous," he told CNN. "There were two days in the desert. No water. No camp. No eating. We could have died."
Like so many here, he just wants to get to Germany, but with the border closed, he simply says: "We pray for God."
And others have ended up at a derelict airport...
The faded carcases of disused planes slowly rust on the tarmac at Athens' old Hellinikon International Airport, a reminder of its former glory when it greeted very different travelers to Athens.
The airport closed in 2001 and part of the vast area was converted into an Olympic park, which according to official figures from the Greek government, is currently sheltering 4,120 people.
Women in headscarves hold babies while young boys and men stand on the balcony of the airport's domestic arrivals hall. They are surrounded by the detritus of lives hastily left behind: piles of old clothes, cardboard boxes, nylon bags.
Most are from Afghanistan, while others come from Pakistan, Iran and Morocco. They have been barred from crossing the border because they are considered to be from "safe" countries.
Inside the airport building, a sea of brightly colored tents and cheap blankets covers every spare foot of the floor, a temporary home for those who have reached Athens but who now face an uncertain future.
Young men try to while away the time any way they can by talking, sleeping on the floor or waiting and thinking. A few feet away, children play with a ball under a sign pointing the way to departures.
Like many of the refugees in Greece today, they are stuck -- not in a refuge but in a purgatory of faded hopes and broken dreams.