It has no running water, and the delivery room is little more than a pair of padded benches with stirrups. But the blue paint on the walls is fairly fresh, and the labor room beds have mosquito nets.

Inside, three generations of the Yankulije family are relaxing on one bed: Rachel, 53, her daughter Chantal Mujawimana, 22, and Chantal’s baby boy, too recently arrived in this world to have a name yet.

The little prince is the first in his line to be delivered in a clinic rather than on the floor of a mud hut. But he is not the first with health insurance. Both his mother and grandmother have it, which is why he was born here.

Rwanda has had national health insurance for 11 years now; 92 percent of the nation is covered, and the premiums are $2 a year.

Sunny Ntayomba, an editorial writer for The New Times, a newspaper based in the capital, Kigali, is aware of the paradox: his nation, one of the world’s poorest, insures more of its citizens than the world’s richest does.

He met an American college student passing through last year, and found it “absurd, ridiculous, that I have health insurance and she didn’t,” he said, adding: “And if she got sick, her parents might go bankrupt. The saddest thing was the way she shrugged her shoulders and just hoped not to fall sick.”

For $2 a year, of course, Rwanda’s coverage is no fancier than the Mayange maternity ward.

But it covers the basics. The most common causes of death — diarrhea, pneumonia, malaria, malnutrition, infected cuts — are treated.

Local health centers usually have all the medicines on the World Health Organization’s list of essential drugs (nearly all are generic copies of name-brand drugs) and have laboratories that can do routine blood and urine analyses, along with tuberculosis and malaria tests.

Ms. Mujawimana gave birth with a nurse present, vastly increasing the chances that she and her baby would survive. Had there been complications, they could have gone by ambulance to a district hospital with a doctor.

“In the old days, we came here only when the mother had problems,” her mother said. “Now the village health worker orders you not to deliver at home.”

Since the insurance, known as health mutuals, rolled out, average life expectancy has risen to 52 from 48, despite a continuing AIDS epidemic, according to Dr. Agnes Binagwaho, permanent secretary of Rwanda’s Ministry of Health. Deaths in childbirth and from malaria are down sharply, she added.

Of course, many things that are routine in the United States, like M.R.I. scans and dialysis, are generally unavailable. Cancer, strokes and heart attacks are often death sentences. The whole country, with a population of 9.7 million, has one neurosurgeon and three cardiologists. (By contrast, New York City has 8 million people; at a national softball tournament for neurosurgeons in Central Park 10 days ago, local hospitals fielded five teams.)

(In another contrast with the United States, obesity and its medical complications are almost a nonissue. Visitors to Rwanda are quickly struck by how thin everyone on the street is. And it is not necessarily from malnutrition; even the president, Paul Kagame, a teetotaling ascetic, is spectral.)

General surgery is done, but waits can be weeks long. A few lucky patients needing advanced surgery may be treated free by teams of visiting doctors from the United States, Cuba, Australia and elsewhere, but those doctors are not always around. Occasionally, the Health Ministry will pay for a patient to go to Kenya, South Africa or even India for treatment.

Still, even with rationing this strict, how can any nation offer so much for $2 a year?

The answer is: It can’t. Not without outside help.

Partners in Health, the Boston-based health charity, which runs two rural hospitals and a network of smaller clinics in Rwanda, said its own costs ran $28 per person per year in areas it serves. It estimated that the government’s no-frills care costs $10 to $20.

According to a study recently published in Tropical Medicine & International Health, total health expenditures in Rwanda come to about $307 million a year, and about 53 percent of that comes from foreign donors, the largest of which is the United States. One big donor is the Global Fund to Fight AIDS, Tuberculosis and Malaria, which is experimenting with ways to support whole health systems instead of just treating the three diseases in its name. It pays the premiums for 800,000 Rwandans officially rated as “poorest of the poor.”

In a nation of poor farmers, who is officially poorest is decided by village councils. They weigh assets like land, goats, bicycles and radios and determine whether a hut has a costly tin roof or just straw.

“People know their neighbors here,” said Felicien Rwagasore, a patient coordinator at the Mayange clinic. “They do not make mistakes.”

Making every Rwandan pay something is part of President Kagame’s ambitious plan to push his people toward more self-reliance and, with luck, eventually into prosperity. The country has been called “Africa’s Singapore.” It has clean streets and little crime, and each month everyone does one day of community service, like planting trees. Private enterprise is championed, and Mr. Kagame has been relentless about punishing corrupt officials. In the name of suppressing remarks that might revive the hatreds that spawned the 1994 genocide, his critics say, he suppresses normal political dissent, too.

A more practical obstacle to creating a health insurance system, however, is that most of the world’s poor, including Rwanda’s, resist what they see as the unthinkable idea of paying in advance for something they may never get.

“If people pay the $2 and then don’t get sick all year, they sometimes want their money back,” said Anja Fischer, an adviser to the Health Ministry from GTZ, the German government’s semi-independent aid agency.

Also, the co-pays can be overwhelming. Even $5 for a Caesarean section can be too much for people as close to the edge as the Yankulijes, who live by growing beans and sweet potatoes and wear American castoffs (Mrs. Yankulije’s T-shirt read “Wolverines Football”).

Many live by barter and cannot scrape together even $2 in coins, said Dr. Damas Dukundane, who works in a poor rural area. Since the government accepts only cash, he said, his patients sometimes go to traditional healers, who could be dangerous quacks but will take goats or chickens.

As a result of all these factors, Rwanda is a patchwork of small clinics, some richer or better-run than others. Mayange’s, for example, gets donations and guidance from the Access Project founded by Josh N. Ruxin, a Columbia professor of public health who now lives in Kigali.

For example, the computer that prints the insurance cards has a Webcam on it. Previously, Professor Ruxin said, for insurance costing $2, villagers had to bring in photographs that had cost them $1 or more.

A clearer example of how the system overburdens the poor, he said, was the fact that the wealthiest Rwandans pay the same $2 that the rural poor do.

Dr. Binagwaho, the Health Ministry official, agreed.

“It’s totally insane that my mother pays the same as the woman who cleans her house,” she said. “That law is being changed.”

Still, Dr. Binagwaho said, Rwanda can offer the United States one lesson about health insurance: “Solidarity — you cannot feel happy as a society if you don’t organize yourself so that people won’t die of poverty.”