Should your ZIP code determine your future? Not according to American ideals of social mobility. American realities, however, tell a different story: Where people grow up goes a long way toward shaping how well they will be educated, how stable their families will be, how high their dreams can soar.

Perhaps no group knows this better than impoverished African-Americans often trapped in soul-deadening public housing, the segregated “projects” that have dotted many an urban landscape. Breaking entrenched patterns of racial separation has been a decades-long challenge for the government. Now the Obama administration, in its final months, is pursuing a fresh solution: a plan that puts ZIP codes front and center.

But to see where we may be headed, it is important to know where we have been. That is the mission of Retro Report, a series of video documentaries examining major news stories of the past and their continued resonance. This episode harks back 50 years, to a federal lawsuit in Chicago that sought to put a dent in enforced segregation by offering black families a path out of unsafe, unhealthy and unsparing inner-city projects.

The case came to be known as Gautreaux, named for its lead plaintiff, Dorothy Gautreaux. She and others accused the Chicago Housing Authority of discrimination in its stewardship of public housing that methodically steered low-income minorities toward ghettos. The lawsuit led 10 years later to an 8-to-0 Supreme Court ruling that declared this segregation unacceptable and said the courts could compel cities to create housing for the poor in wealthier — read: whiter — suburbs.

What evolved in Chicago was a system of vouchers for poor black families that subsidized moves to more prosperous neighborhoods. Ms. Gautreaux did not live long enough to reap the benefits, but her name endured: The initiative was called the Gautreaux Assisted Housing Program.

To keep whites from fleeing en masse — hardly an unknown response to a sudden influx of minorities — the program kept the number of voucher families low for any single suburban town. From 1976 to 1996, more than 7,000 households were resettled, including Valencia Morris and her three daughters, whose experiences are highlighted in the video. The selection process sought to minimize the possibilities of failure. Certain higher-risk families were excluded, like those with more than four children or with bad credit ratings.

Suburban life for the Morrises was not easy — they had to cope with racial slurs and other humiliations — but they persisted. Some other resettled families gave up and returned to the city, which was still perilous but was at least familiar.

Despite such setbacks, Gautreaux families generally fared well. Studies showed that their children did better in school than those who never left the projects. More of them went to college. They landed higher-paying jobs and were more likely to build two-parent families of their own.

The results encouraged the Clinton administration to take the experiment national in the 1990s with a similar program, Moving to Opportunity, designed to benefit several thousand households in Baltimore, Boston, Chicago, New York and Los Angeles. There was one big difference from Gautreaux: Only some families got vouchers designed specifically for moves to the suburbs. Others received aid but essentially had to stay where they were. Still others that took part in the project got no vouchers

The assumption was that Moving to Opportunity, like Gautreaux, would cause suburbanized households to outperform their public-housing counterparts. It did not work out that way. A decade later, researchers detected no significant difference in achievement between children who had moved to wealthier neighborhoods and those who had not.

And that seemed to be that. Only it wasn’t.

Moving to Opportunity faded away, but social scientists who explored it more deeply after nearly another decade found reasons for optimism. Yes, children who were taken from the projects to the suburbs in their teens did not do so well; teenagers are not known for handling disruption gracefully. But their younger brothers and sisters, who spent many more of their formative years in the suburbs, performed noticeably better at school and in future jobs.

ZIP codes counted. “Every extra year of childhood spent in a better neighborhood seems to matter,” Raj Chetty, a Stanford economist who studied the program, has said. Another researcher, the Harvard economist Lawrence F. Katz, told Retro Report: “Neighborhoods and childhood development are long investments, and one has to have some patience. Most things that are investments take a while to pay off.”

Obviously, segregation in America is a complex matter, historically replete with unsavory practices like redlining and blockbusting, and filled with anger and fear on all sides. Many people, both black and white, are less than enchanted with government efforts at integration that they regard as unwelcome social engineering. Even two of Ms. Morris’s daughters, though beneficiaries of suburban childhoods, found as adults that they felt more at home living in a city.

The face of public housing has changed over the years. In some cities, huge public housing projects have been demolished, including notorious complexes like Cabrini-Green, a Chicago monument to violence, degradation and failure.

But hardships remain. A study last year by the Century Foundation found a sharp increase in “concentrated poverty,” a term applied to a census tract where at least 40 percent of the residents are below the federal poverty line — about $24,000 for a family of four. From 2000 to 2013, the foundation said, the number of Americans living in concentrated poverty rose to 13.8 million from 7.2 million, with African-Americans and Latinos disproportionately represented. In major cities like Chicago, Detroit, Milwaukee and Baltimore, daily life is racially separate and decidedly unequal.

Subsidized housing is not the only element in America’s racial mosaic, but it looms large. The Housing Choice Voucher Program, run by the Department of Housing and Urban Development, assists about 2.4 million families with a total of 5.3 million people. Households typically apply 30 percent of their income to the rent, with the government paying the rest.

HUD calculates what it judges to be “fair-market rent” for a broad metropolitan region — a method that, however unintentionally, provides many poor families with subsidies sufficient to lift them into only marginally better neighborhoods, if that. Moving to appreciably more prosperous areas is often impossible.

This is where the Obama administration steps in. Its HUD secretary, Julián Castro, wants to fine-tune how fair-market rent is calculated, by basing it on housing costs in individual ZIP codesrather than in entire regions. Under this methodology, people who find an apartment in a higher-rent zone would have their subsidy increased substantially. A system like this was tried in Dallas, reportedly with fair success.

There is a potential downside: Families that remain in neighborhoods where rents are comparatively low would find their vouchers cut, a prospect that has produced objections from some elected officials, including in New York. They warn that if those subsidies shrink, some poor families will have to pay more out of their own threadbare pockets or be forced to move.

A final decision by HUD is expected this fall. But it is already clear that if there is a constant in life’s game of Chutes and Ladders, it is the consuming importance of one’s ZIP code. No one knows that better than Henry G. Cisneros, the HUD secretary during the Clinton years.

“All of the other forms of segregation that exist in our society,” Mr. Cisneros told Retro Report, “begin with, ‘Where do you live?’”

CLYDE HABERMAN, a regular contributor to Retro Report, has been a reporter, columnist and editorial writer for The New York Times, where he spent nearly 13 years based in Tokyo, Rome and Jerusalem. Subscribe to our newsletter here and follow us on Twitter @RetroReport.

This article first appeared in The New York Times.