LEXINGTON — Evelyn Brito knew how to navigate her tough slice of Dorchester, how to steer her kids around the drug dealers and find a decent piece of fruit in the tired bodegas. But when she heard the gunshots outside her building, well, that was different. She was shaken. She had to go.

It took some time, but Brito managed to find a subsidized apartment in a better-off community. Much better off, in fact: Lexington, a suburb of gracious Colonials and lofty SAT scores about 15 miles northwest of Boston.

Brito has to take a bus and two subways to get to her job in the city now. But the lengthy commute is worth it, she says. Her daughter can play alone in the backyard without fear. And her son, who just started his senior year at Lexington High, is considering St. John’s University in New York. Many of her old neighbors in the city aren’t faring so well. “Some people,’’ she said, “their environment swallows them.’’

Low-income families who use housing subsidies to move from struggling to thriving communities represent perhaps the country’s best shot at breaking intergenerational poverty. Landmark research from Harvard University last year showed that children from poor families who make the transition at a young age are more likely to go to college, less likely to become single parents, and earn more money than those who remain behind.

But despite the success of families like the Britos, their story remains an exception. Relatively little subsidized housing has sprouted in places like Lexington, even as the federal government has underwritten thousands of affordable apartments in poor, racially isolated neighborhoods like the section of Dorchester where Brito and her children once lived.

A Globe examination finds that politics and inertia have conspired to create this lopsided geography of affordable housing — undercutting the region’s best hope for racial and economic integration.

Suburban resistance is a big part of the story.

But it’s also about the well-meaning neighborhood groups that have teamed up with bankers and developers to build so much of the region’s subsidized housing in the most troubled places.

And it’s about the poor themselves, hemmed into distressed neighborhoods not just by the distribution of affordable apartments but by their lack of familiarity with the leafy communities beyond — and their doubts about how they’d fit in.

Researchers at Brandeis University’s Heller School for Social Policy and Management have mapped the whole phenomenon at the Globe’s request. And the results are striking. Just 21 percent of federally subsidized units in Eastern Massachusetts are in so-called high-opportunity neighborhoods, with ready access to jobs, healthy food, and quality schools.

That leaves 79 percent in moderate- and low-opportunity neighborhoods, block after block of housing projects and apartment complexes lining Franklin Park, surrounding Mattapan Square, and filling out struggling sections of Brockton and Lawrence.

Even federal Section 8 housing vouchers, which low-income families can use to rent moderately priced apartments anywhere, are clustered in the poorest communities in the region, the analysis shows.

The imbalance is not just a social concern. It may also be a violation of federal law.

The Fair Housing Act of 1968 requires state and local officials to spend federal housing dollars in ways that actively promote integration. And in recent years, jurisdictions from Marin County, Calif., to Westchester County, N.Y., have faced legal action for their failure to do so.

Henry Korman, a prominent housing and civil rights lawyer in Boston, says the record of subsidized segregation is not much better here.

“We’ve done very badly,’’ he said, tilting back in his office chair on a recent afternoon. “It’s really pretty shameful.’’

Newton Mayor Setti Warren was worried.

In a week, he would release an ambitious blueprint for hundreds of new market-rate and affordable housing units that was sure to add fuel to an already smoldering debate over who is welcome in his well-to-do suburb and who is not.

“This is going to be really hard,’’ he said, sitting at a long, rectangular table in his City Hall office that June morning.

Harder, even, than he knew.

The glittering band of suburbs bending around Boston has long been torn between a liberal impulse to help the poor and a powerful desire to protect its rolling lawns against any sign of encroachment.

And nowhere has the tension been more pronounced than in Newton, a handsome collection of 13 villages just outside Boston.

The city was home to one of the nation’s first organized efforts to build affordable housing in the suburbs, a foundation formed in 1968 by a band of priests, rabbis, and ministers determined to erect 500 federally financed units for those of modest means.

Leaders of the effort were hopeful, at the start, that the community would embrace it. But when the foundation announced the actual sites it was proposing for the housing, the city recoiled.

Angry letters filled the local newspaper. Protest filled the aldermen’s chamber. And eventually, 500 units turned into 50. “I guess it’s true,’’ one affordable housing advocate lamented at the time, “that liberalism stops at your own driveway.’’

The foundation managed to add dozens more units in the decades that followed. But Newton, like scores of other suburbs, has consistently fallen short of state-set goals for affordable housing production.

Since Warren took office in 2010, just 18 below-market units have been built in the city, with another 33 under construction. The meager numbers have been a source of embarrassment for the mayor, an ambitious Democrat who has long held out Newton as a place of tolerance and opportunity.

His own parents, as he often notes, came to the city in search of good schools, safe streets, and a community that would welcome a black couple from Harlem and the Bronx. “That is who we are,’’ he said, speaking broadly of the city’s values.

But affordable housing advocates doubt the mayor’s sincerity.

It was just three years ago that he withheld federal housing funds for a nine-unit development for the chronically homeless planned for a long-decommissioned fire station in Waban, a wealthy village on the west end of town where the locals play tennis at The Windsor Club in the summer and sled at Brae Burn Country Club in the winter.

“We live in a community where our kids walk to school,’’ one neighbor said at a public hearing on the project, “and I want to know why we shouldn’t be worried.’’ Another suggested that the prospective tenants might be more comfortable, “I hate to say this, but in Waltham.’’

After the project collapsed, affordable housing advocates filed a complaint with the US Department of Housing and Urban Development, alleging that the city had violated the Fair Housing Act by accommodating neighbors’ discriminatory views.

Last year, the parties reached a settlement, with the city agreeing to create 9 to 12 units for the homeless by 2020. But it did little to quiet the noisy debate over affordable housing in Newton. If anything, it added to the din.

Critics of the relatively modest HUD agreement saw a sign of something bigger to come. A high-profile settlement in Westchester County, N.Y., was planting hundreds of affordable houses and apartments in that iconic stretch of suburbia just north of New York City.

And when HUD issued a new rule last year designed to press more communities into meeting their legal obligation to integrate, conservative commentators warned of a “war on the suburbs,’’ with Washington poised to impose big, mixed-income developments on plush town greens.

“It’s now gotten to the point where if you say, ‘I like a single-family house and a lawn,’ you’re a racist,’’ said Kathleen Kouril Grieser, a lead organizer with a group called the Newton Villages Alliance that has opposed some development in town. “How did that happen?’’

Grieser sharply opposes Warren’s new housing plan. But in a blow to the mayor, affordable housing advocates have also refused to get on board.

They say they can’t back a push for hundreds of new units when the administration hasn’t shown enough progress toward building the 9 to 12 laid out in the HUD settlement.

Andrea Kelley, a landscape architect and affordable housing activist, said she and a couple of others delivered the news in a private meeting with the mayor just off his City Hall office. And it did not go well.

Warren grew frustrated, she said, turning on another advocate in the room. “He was yelling at her and she was trying to finish her point and she would say, ‘With all due respect Mr. Mayor, please let me finish what I’m trying to say,’ and he would scream at her, ‘No, I’m going to tell you,’ ’’ she said.

The mayor denies that he raised his voice. But one thing was clear: When the meeting came to a close, Newton’s long-flagging attempts to build affordable housing had suffered another setback.

State lawmakers did take a big swipe, once, at suburban resistance to affordable housing.

It’s called Chapter 40B, the so-called anti-snob zoning law, and the Legislature passed it in the summer of 1969, just a year after the assassination of Martin Luther King Jr. and the Kerner Commission’s stark warning of a nation “moving toward two societies, one black, one white — separate and unequal.’’

The statute was, by any measure, pioneering: a first-of-its-kind attempt to confront the exclusionary practices of white, wealthy suburbs.

The law allows developers to bypass local zoning restrictions in towns without a threshold amount of affordable housing in place, as long as they agree to set aside 20 to 25 percent of their units for lower-income families.

And over the past half-century, the measure has had some success — coaxing the construction of about 35,000 below-market-rate units, even in communities like Newton where resistance can be fierce.

But advocates say that success has masked a critical shortcoming: The state’s signature effort to open up its most affluent communities doesn’t do enough to draw in the truly poor.

There was, to be sure, an early push to build several thousand units for very low-income families — apartments that still provide a certain number of struggling single mothers in Lowell and Lynn a chance to escape to the suburbs and enroll their children in high-achieving schools.

But for decades now, state regulations have steered many of the affordable apartments to moderate-income families — up to $73,050 for a family of four, at last count. That’s carpenters and office assistants and retail clerks — working people who may be in need of affordable housing, but not necessarily the transformative experience an upscale community can offer the truly disadvantaged.

Many of the apartments erected in the suburbs, moreover, are for seniors rather than the families with kids who could most benefit from the shot at upward mobility.

Fifty-five percent of the affordable housing in Eastern Massachusetts’ suburban communities is reserved for older people, according to an analysis conducted by the Citizens’ Housing and Planning Association for the Globe, compared with just 39 percent in the region’s cities.

Jennifer Van Campen, an affordable housing developer with Metro West Collaborative Development in Newton, said she occasionally talks with allies about trying to recalibrate the law so it serves more low-income families. But “any time I talk to people about trying to strengthen and improve 40B,’’ she said, “they look at me like I have three heads.’’

Advocates, Van Campen said, are leery of opening up the statute to revision when suburban lawmakers are so eager to dilute it.

Those attempts at dilution have mostly failed. And a few years ago, a ballot measure aimed at repealing the law altogether fell short. But the wealthiest communities have sought other ways around the statute.

Lately, a handful of suburbs have invoked an exemption for towns that have built affordable housing on 1.5 percent or more of their developable land. Among them: Newton, which tried to make the numbers work by contending that three private golf courses were open space, exempt from the calculation.

A state housing appeals committee rejected that argument when the city invoked it in the midst of a tense debate over a proposed mixed-income development in the Auburndale section of town. But it contributed to lengthy delays on the project. And earlier this year, developer Scott Oran simply pulled the plug.

He’s still irritated by the whole affair. “I think that’s the most cynical interpretation that I’ve ever heard,’’ he said, “using golf courses to keep out low-income people.’’

The Orchard Park public housing project in Roxbury was a grim place. Shattered glass. Dead-end streets. In the late-1980s, a drug kingpin known simply as “God’’ ruled over the complex outside Dudley Square.

Now, a collection of trim, colorful town houses called Orchard Gardens stands in its place. Bouquets of flowers brighten the porches, and white chairs glint in the sun. “This was a place of despair,’’ said Jeanne Pinado, standing at the heart of the development on a recent morning, “and you can see what it is now.’’

Pinado is chief executive of the Madison Park Development Corporation, a neighborhood nonprofit that helped build Orchard Gardens in the late 1990s with the assistance of a large federal grant.

Over the last half-century, Madison has overseen the construction of about 1,000 affordable apartments in the neighborhood — scattered among big, brick towers and squat, wood-frame row houses. For many, the developments are a source of pride: a symbol of self-empowerment in a neighborhood that was long neglected by city officials.

But in recent years, this pattern of housing development has faced mounting criticism from civil rights advocates and academics who say it locks too many poor people into poor neighborhoods, no matter how attractive the pastel exteriors and energy-efficient appliances.

Myron Orfield, director of the Institute on Metropolitan Opportunity at the University of Minnesota, has emerged as a leading critic of what he calls the “poverty housing industry’’ that has built it all.

Community development corporations like Madison Park, however well-meaning, are myopic, he says, “looking at the world one block or two blocks at a time’’ and missing larger concerns about segregation.

The big-name financial institutions that invest in the federal low-income housing tax credits that power the bulk of subsidized housing projects are seeking an easy way to meet their legal obligations to invest in high-poverty neighborhoods, he says.

And the developers that do the actual building, he says, are reaping tidy profits in communities where resistance is scant.

There are “two partners in racial segregation,’’ Orfield says. “One is white opposition — NIMBYism — and the other is the poverty housing industry. And they shake hands across the table.’’

James Keefe, a principal with Trinity Financial, a development firm that partnered with Madison Park on the Orchard Gardens project, acknowledges that low-income neighborhoods provide the path of least resistance.

But a good building in a distressed area, he says, can be transformative.

“You make something beautiful and thoughtful that isn’t an army barracks with prison bars in the windows — you design to people’s better instincts — and, more often than not, people respond well to that,’’ Keefe says.

And the buildings, he points out, don’t stand alone. In Dudley Square, Madison Park has complemented its acres of affordable housing with job training, financial literacy courses, and a performing arts center with a visiting playwright.

Supporters of this sort of urban “placemaking’’ say it is a vital part of any credible antipoverty strategy; policy makers, after all, can’t just abandon big, poor neighborhoods in their zeal to integrate the suburbs.

But critics say the heavy reliance on inner-city revitalization is hard to justify when there is little evidence that such sweeping efforts to turn around poor neighborhoods actually boost incomes or improve school performance.

Pamela Rhodes Cannon has seen the stubborn quality of entrenched poverty up close.

She moved into the big patch of subsidized housing outside Dudley Square 33 years ago, and she quickly went about trying to improve the place.

She built a tenants association and helped start a fall festival. She counseled the neighborhood kids after shootings. And when she had a school cafeteria job, she brought them bags of leftover apples and chicken sandwiches.

“I’m telling you,’’ said Cannon, 55, strolling down the block on a recent afternoon, “I raised this whole neighborhood.’’

But after decades of committee meetings and Unity Day celebrations, it has all begun to feel a little fruitless. There are still too many dangerous blocks in her subsidized village and the tough neighborhood just beyond, she says. And many of the kids Cannon coached through adolescence have struggled to move up and out as young adults.

Her own daughter, determined to leave subsidized housing, is still in it for now — just a couple of blocks away, raising a young girl.

Cannon, sitting on the couch in her modest living room, said: “Sometimes I feel like there are too many of these apartments together.’’

It was a bombshell ruling.

In the summer of 1989, more than a decade after the Boston chapter of the NAACP filed a lawsuit aimed at dismantling the region’s deep legacy of housing segregation, a federal judge had finally ruled for the civil rights organization.

Dianne Wilkerson, a lawyer for the NAACP who would later become a state senator, declared it “a blockbuster — a whole new world’’ that “changes life for minorities in Boston in some very major ways.’’

The ruling spawned 500 new special federal Section 8 housing vouchers, tailored to move minority families, at least for a time, into predominantly white and generally better-off communities.

It was, it seemed, an opportunity for the sort of integration that could change lives. That opportunity, though, would never be fully realized.

The number was modest compared with the scope of the problem; tens of thousands live in the city’s most segregated neighborhoods. And money to counsel people searching for their new homes soon ran out.

Today, scores of the so-called Skinner vouchers, named after the judge in the case, sit unused. And only about one-quarter of those in circulation are still paying for apartments in predominantly white communities, with many voucher holders drifting back to the poor, mostly minority neighborhoods they’d known their whole lives.

The problems with the Skinner vouchers speak to the limitations of the larger federal Section 8 voucher program — an engine of mobility that has not moved participants very far at all.

Created in 1974, it was seen as an antidote to the country’s bleak housing projects: a ticket out of the big “vertical ghetto.’’

Nationwide, about 2.2 million poor families use the vouchers to rent moderately priced apartments, with the subsidy amount adjusted according to family size and local housing costs. And in Massachusetts, one of a handful of states where landlords are required to accept the vouchers, the potential to open up thriving neighborhoods to the poor is particularly pronounced.

But the Brandeis analysis of Greater Boston, conducted for the Globe, finds the same lopsided geography for Section 8 vouchers as for brick-and-mortar subsidized apartments. Just 19 percent of voucher holders live in high-opportunity neighborhoods, researchers found, while 81 percent reside in moderate- and low-opportunity neighborhoods.

Studies show a similar imbalance elsewhere in the country. Researchers point to two major factors: the limited horizons of poor people who have not spent much time outside their own neighborhoods, and policies that make it even more difficult for them to extend their search.

When public housing agencies issue vouchers, for instance, they generally give recipients 60 days to find an apartment, with extensions in some cases — time quickly consumed touring substandard apartments and waiting for return calls from landlords.

Facing a rapidly approaching deadline, voucher holders increasingly rely on websites like gosection8.com or referrals from friends and relatives, steering them back to the racially and economically segregated neighborhoods they know best.

But research suggests there is a way to clear these hurdles, to nudge willing, low-income families into better-off neighborhoods — a tantalizing path to mobility pursued by surprisingly few major US cities.

Yvette Appiah stands at the front of a small classroom in downtown Baltimore, looking out at 32 women from the poorest and most segregated parts of the city — boarded-up row houses stretching out for blocks on end, some propped up by posts and others with rotted-out roofs.

All are here for their next counseling session with the Baltimore Housing Mobility Program, an outgrowth of a sweeping housing desegregation lawsuit filed by the Maryland chapter of the American Civil Liberties Union.

It is a cousin of the kind of training program for needy home-seekers that grew up in Boston after the NAACP litigation, then fizzled for want of funds. Baltimore is showing what a sustained commitment to such an effort can do.

The program moves families out of low-opportunity areas, marked in orange on the maps hanging on the classroom walls, and into high-opportunity areas, marked in green — a slice of north-central Baltimore City and big swaths of Baltimore, Harford, Howard, Carroll, and Anne Arundel counties.

About 3,300 families have made the move over the 14-year life of the program, and some three-quarters of them remain in high-opportunity areas today. By the end of 2018, the program will have reached almost 4,400 families.

The idea is simple: provide participants with months of training before they receive their vouchers, giving them a better shot at moving to more prosperous neighborhoods and staying there long-term.

Participants work with counselors to repair their credit. They learn to care for hardwood floors. And they pile into minivans to tour the suburbs, visiting apartments they might rent and driving past the local elementary school and doctor’s office.

Today, they are attending Appiah’s seminar on how to conduct an effective housing search — two hours of practical tips sprinkled with notes of encouragement.

Her first tip: Buy a notebook at Walmart for 50 cents and use it to organize your search. Jotting down an appointment on the corner of a stray envelope and tucking it into your purse, she suggests, just won’t do.

“I’ve seen some of your purses,’’ she says, drawing chuckles. “They look like mine.’’

Appiah walks through the room, handing out the sort of apartment-for-rent advertisers available at supermarkets. Then, she offers some pointers on Internet searching.

The housing mobility program requires participants to live in high-opportunity communities for at least two years after they receive their vouchers, and Appiah takes them to one now — clicking through photographs for a development called “Lake Village Townhomes’’ in Severn, a suburb south of Baltimore.

“I like the fridge and stove,’’ she says.

And then: “Oh look, tennis court — take up a new hobby.’’

But if the amenities are inviting, Appiah warns her charges, don’t get too caught up in them. It’s the community that matters, she says. The schools. The peace of mind that comes with a safe neighborhood.

“How many of you came into orientation telling me you can’t let your kids go out and play?’’ she asks. Half of the women in the room raise their hands.

“Right,’’ says Appiah. “So how major is that going to be to you as a parent — as a single parent — to just let your kids go out to the playground?’’

The growing focus on mobility has revived interest in counseling programs in Greater Boston.

Officials with the Boston Housing Authority, one of several government agencies and nonprofits in the region that administer Section 8 vouchers, say they are looking to direct some of their funding toward this kind of effort.

For now, though, voucher recipients in Eastern Massachusetts are mostly on their own. And getting out of tough neighborhoods is often not their first priority.

When Shantel Young of Dorchester got her subsidy this winter after a decade-long wait, she was more concerned with finding a place big enough for her growing family, on a relatively safe block.

“I know things happen everywhere,’’ she said, but “I want to make sure that wherever we move, it isn’t, like, drug activity at the front door.’’

Even with those modest expectations, though, her search quickly turned frustrating.

One landlord accepted Young, her husband, and her two kids for a Dorchester apartment and then changed his monthly asking price from $1,900 to $2,000, just over what they could afford with their government subsidy.

When a second apartment seemed within grasp, Young, 28, started packing — taking down the curtains, boxing up the family pictures, and removing a favorite prayer from the wall: “God, grant me the serenity to accept the things I cannot change . . .’’ But the place, it turned out, was not deleaded as promised.

Young, sitting among her boxes of dishes and clothes in a worn apartment building alongside Franklin Park, was growing increasingly anxious.

The window to use her long-sought voucher was closing, and the search process had become overwhelming.

“I feel like quitting,’’ she told her husband at one point during the housing hunt, her eyes filling with tears.

Hitting dead end after dead end, she thought briefly about looking for a place in suburban Norwood, where her in-laws lived. She’d seen some housing complexes out there that she liked, with pools and fitness centers.

But searching in Norwood, she learned, would require transferring jurisdiction of her voucher from one agency to another. “And right then, I was like, ‘Oh no, that’s just more stuff, I’m not even going to do it,’ ’’ she said, sitting on her living room couch with her 7-month-old daughter on her lap.

As Young spoke that May morning, she was finally closing in on the place her family would land — a spacious Dorchester duplex, with three bedrooms spread out over two floors and a driveway on the side.

A month later, she would move into the place, all those packing boxes finally finding a home just a few blocks from her old place. Safe enough, but still surrounded by poverty and, not so far off, a bustling drug trade.

“The area is not really where I want to be,’’ she said, “but it’s better than nothing.’’

Young paused for a moment, thinking back on a trying and sometimes lonely search for a new home. It was good to be done, at least.

“I’m just glad,’’ she said, “that the search is over.’’

One in a series of occasional articles examining how income disparities are reshaping the region

David Scharfenberg can be reached at david.scharfenberg@globe.com. Follow him on Twitter @dscharfGlobe.