Fredric J. Brown / AFP / Getty A nurse checks the name tags on babies after they are given a bath at a hospital in Beijing

Is the world's most populous nation about to get more crowded? Reports surfaced in international media last week that in an effort to slow the rapid graying of the workforce, couples in Shanghai  the country's most populous city  would be encouraged to have two kids if the parents are themselves only children. Shanghai officials have since denied any policy shift, saying this caveat is nothing new, but the contradictory reports are another manifestation of ongoing rumors that Beijing is rethinking the controversial one-child policy that has for the past three decades helped spur economic growth  but exacted a heavy social cost along the way. (See TIME's China Blog.)

Soon after the founding of the People's Republic of China, improved sanitation and medicine prompted rapid population growth that  after a century of wars, epidemics and unrest  was initially seen as an economic boon. "Even if China's population multiplies many times, she is fully capable of finding a solution; the solution is production," Mao Zedong proclaimed in 1949. "Of all things in the world, people are the most precious." The communist government condemned birth control and banned imports of contraceptives. (Read a TIME cover story on China's growing power.)

Before long, however, population growth was taking a toll on the nation's food supply. In 1955 officials launched a campaign to promote birth control, only to have their efforts reversed in 1958 by the Great Leap Forward  Mao's disastrous attempt to rapidly convert China into a modern industrialized state. "A larger population means greater manpower," reasoned Hu Yaobang, secretary of the Communist Youth League, at a national conference of youth work representatives that April. "The force of 600 million liberated people is tens of thousands of times stronger than a nuclear explosion."

It also proved to be nearly as destructive: with many communities collectivized and converted from farming to steel production, food supply slipped behind population growth; by 1962 a massive famine had caused some 30 million deaths. In the aftermath, officials quietly resumed a propaganda campaign to limit population growth, only to be interrupted by the turmoil of the Cultural Revolution in 1966; it began it again in 1969. A push under the slogan "Late, Long and Few" was successful: China's population growth dropped by half from 1970 to 1976. But it soon leveled off, prompting officials to seek more drastic measures. In 1979 they introduced a policy requiring couples from China's ethnic Han majority to have only one child (the law has largely exempted ethnic minorities). It has remained virtually the same ever since.

The one-child policy relies on a mix of sticks and carrots. Depending on where they live, couples can be fined thousands of dollars for having a supernumerary child without a permit, and reports of forced abortions or sterilization are common. (Blind rural activist Chen Guangcheng made international headlines in 2005 for exposing just such a campaign by family-planning officials in Eastern China; he was later imprisoned on charges his supporters say were retaliatory.) The law also offers longer maternity leave and other benefits to couples that delay childbearing. Those who volunteer to have only one child are awarded a "Certificate of Honor for Single-Child Parents." Since 1979, the law has prevented some 250 million births, saving China from a population explosion the nation would have difficulty accommodating.

But critics of the policy note its negative social consequences, particularly sex discrimination. With boys being viewed as culturally preferable, the practice of female infanticide  which had been common before 1949 but was largely eradicated by the 1950s  was resumed in some areas shortly after the one-child policy went into effect. The resulting gender imbalance widened after 1986, when ultrasound tests and abortions became easier to come by. China banned prenatal sex screening in 1994. Nonetheless, an April study published in the British Medical Journal found China still has 32 million more boys than girls under the age of 20. The total number of young people is a problem as well; factories have reported youth-labor shortages in recent years, a problem that will only get worse. In 2007 there were six adults of working age for every retiree, but by 2040 that ratio is expected to drop to 2 to 1. Analysts fear that with too few children to care for them, China's elderly people will suffer neglect.

Facing growing resistance to the law, some Chinese officials have turned to harsh enforcement tactics. In 2007, for instance, bureaucrats reportedly took sledgehammers to a half a dozen towns, threatening to whack holes in the homes of people who had failed to pay fines for having too many children. Elsewhere, officials were accused of forcing pregnant women without birthing permits to have abortions and jacking up the fines for families disobeying the law. As a result, riots broke out. As many as 3,000 people demonstrated in Guangxi province, some overturning cars and burning government buildings. Several people may have been killed.

Despite rumors in early 2008 that the one-child policy would be overturned, in May of that year China's top population official said it would not be eliminated for at least a decade, when a large demographic wave of childbearing-age citizens is expected to ebb. For some Shanghai couples, at least, a small measure of change has come sooner.

See TIME's China covers.