To get more attentive care in the country’s national health system, Greeks routinely pay doctors cash on the side, a practice known as “fakelaki,” Greek for little envelope. And bribing government officials to grease the wheels of bureaucracy is so standard that people know the rates. They say, for instance, that 300 euros, about $400, will get you an emission inspection sticker.

Some of the most aggressive tax evaders, experts say, are the self-employed, a huge pool of people in this country of small businesses. It includes not just taxi drivers, restaurant owners and electricians, but engineers, architects, lawyers and doctors.

The cheating is often quite bold. When tax authorities recently surveyed the returns of 150 doctors with offices in the trendy Athens neighborhood of Kolonaki, where Prada and Chanel stores can be found, more than half had claimed an income of less than $40,000. Thirty-four of them claimed less than $13,300, a figure that exempted them from paying any taxes at all.

Such incomes defy belief, said Ilias Plaskovitis, the general secretary of the Finance Ministry, who has been in charge of revamping the country’s tax laws. “You need more than that to pay your rent in that neighborhood,” he said.

He said there were only a few thousand citizens in this country of 11 million who last year declared an income of more than $132,000. Yet signs of wealth abound.

“There are many people with a house, with a cottage in the country, with two cars and maybe a small boat who claim they are earning 12,000 euros a year,” Mr. Plaskovitis said, which is about $15,900. “You cannot heat this house or buy the gas for the car with that kind of income.”

Image Athenians declared taxes at a local office. Greek’s shadow economy represents 20 to 30 percent of its G.D.P. Credit... Yoray Liberman for The New York Times

The Greek government has set a goal for itself of collecting at least $1.6 billion more than last year — a modest goal, Mr. Plaskovitis believes. But European Union officials were so skeptical, Mr. Plaskovitis said, they would not even allow the figure to be included in the budget forecast used in negotiations over the bailout package.