Halfway into an ambitious five-year campaign to end homelessness among veterans, the Department of Veterans Affairs says it has made enough progress that the goal is within reach, even as a new generation of veterans returns from Iraq and Afghanistan.

Making aggressive use of a voucher program, Veterans Affairs has housed more than 33,000 veterans in the past 21 / 2 years. It did so by changing its longtime policy of requiring homeless veterans to be successfully treated for substance abuse and mental ailments before being given apartments.

The shift in approach means that there is “a better opportunity to end veterans’ homelessness by 2015 than at any time in the past,” said Susan Angell, VA’s director of homeless initiatives.

Although many agencies, including the Department of Housing and Urban Development, have adopted a housing-first strategy, Veterans Affairs had resisted. “Folks were initially concerned about the safety aspects of it,” Angell said. “We wanted to make sure they were clean and sober.”

VA and HUD want enough funds to issue 60,000 vouchers at the rate of 10,000 a year through 2014.

The effort comes as tens of thousands of troops who served in Iraq and Afghanistan are leaving military service and entering an often bleak job market.

“For this new generation of veterans, we are very concerned,” Angell said.

Her agency estimates that more than 20,000 Iraq and Afghanistan veterans have been homeless at some point during the past five years and that their numbers are rising.

The agency’s goal is to get all chronically homeless veterans into permanent supportive housing; prevent at-risk veterans from becoming homeless; and get new cases off the streets as soon as possible.

Many Iraq and Afghanistan veterans at risk of homelessness keep a low profile. “They’d rather be off in the shadows,” said Freddy Cordova, a former Army paratrooper who deployed four times to Iraq and now works with a National Veterans Foundation “street team” that helps homeless veterans in California.

Matt Barnes, a 28-year-old former Marine corporal, is representative of this new generation. On a rainy December night, Barnes slipped quietly into St. George’s Episcopal Church in Arlington County, gratefully accepting a bowl of meat stew offered by volunteers and taking a seat at a table with other homeless veterans.

Barnes, who wore a bushy black beard and a donated red sweatshirt, has been homeless for two years since losing his job as a waiter and being unable to afford his apartment in Fairfax County. Barnes served five years in the Marine Corps, including a tour in Fallujah, Iraq, in 2004 during the height of the insurgency, when he regularly risked roadside bombings as a convoy driver.

“It was easier over there,” Barnes mused. He wonders whether he has post-traumatic stress disorder, but he is not interested in going to Veterans Affairs for testing. Instead, Barnes stays on the streets of Northern Virginia, moving between favored locations where he feels safe and grabbing occasional meals and showers in shelters. “I like to be a ghost,” he said.

Barnes finds it nearly impossible to look for a job while homeless. “You can’t get good sleep on the street,” he said. He lacks a phone or even money to get a haircut.

The poverty rate for veterans ages 18 to 34 reached 12.5 percent in 2010, more than double that of 10 years earlier, according to a report last month from Congress’s Joint Economic Committee.

The key to dealing with the Iraq-Afghanistan generation will be keeping veterans off the street in the first place. “People don’t become homeless immediately,” said Dennis Culhane, a University of Pennsylvania professor and authority in the field. “It takes a few years. So we have time to prepare.”

A VA prevention program begun in 2011 is awarding $160 million in grants to nonprofit community agencies, with the goals of preventing low-income families from falling into homelessness or rapidly returning them to stable housing. “We’ve learned we can’t end homelessness by street rescues alone,” said VA Secretary Eric K. Shinseki.

The most effective remedy, advocates say, is the joint voucher program, HUD-VASH, which provides permanent supportive housing to needy homeless veterans.

Veterans pay 30 percent of their income to rent, and the voucher covers any rent above that amount. Each voucher costs the government on average $6,500 a year, plus $4,148 in case management services — much less than the costs of staying in jails, hospitals or emergency shelters, advocates say.

Recipients face regular reviews to make sure they continue to qualify based on income and health-care needs; at some point they may transition to regular low-income housing vouchers.

“It literally saved me,” said Mickiela Montoya, who served with the Army National Guard in Iraq and received a voucher last year for an Orange County, Calif., apartment where she lives with her 4-year-old daughter.

The vouchers are distributed to public housing authorities across the country based on need. “The problem is there are always new people coming into the system, and there aren’t that many vouchers to give out,” said Kathy Sibert, executive director of Arlington Street People’s Assistance Network, or A-SPAN.

Veterans are waiting for vouchers in virtually all jurisdictions across the country, according to Veterans Affairs officials.

Gary Bush, a homeless 54-year-old Navy veteran in Arlington whose hollow cheeks and sunken eyes tell of long nights on the streets, has asked for a voucher, but he was discouraged by the response. “They tell me the waiting list is 500 deep,” Bush said while eating stew at St. George’s provided by A-SPAN.

“In some cases, [vouchers] are going to people that are easiest to house, and not to the person who’s been on the street the longest and has the most issues,” said Jake McGuire, a spokesman for Community Solutions, an advocacy group for the homeless.

VA officials acknowledge the concern and have reminded field offices that the vouchers are meant primarily for chronically homeless veterans with mental health or substance-abuse problems. But the vouchers are generally given to any qualifying homeless veteran on a first-come, first-served basis.

Those selected often must wait four months to a year for housing, depending on the amount of paperwork required by the jurisdiction, said Becky Kanis, who directs a homeless project run by Community Solutions.

In addition, it has been difficult to gauge the problem and measure progress. For years, the VA used what one researcher called “wacky counting” of homeless veterans. Addressing the National Coalition for Homeless Veterans in June, Shinseki asserted that the number of homeless veterans had been reduced in two years from 131,000 to 76,500. VA officials now acknowledge the numbers were not comparable.

Culhane, who also is director of research for VA’s National Center on Homelessness Among Veterans, said the numbers are now much more accurate, with a 2011 count of homeless veterans on a given night conducted by teams in 432 communities nationwide.

VA and HUD officials hailed the new figures this month, a 12 percent drop in the one-night count of homeless veterans, from 76,329 on a single night in January 2010 to 67,495 in January 2011.

But even if all homeless veterans could be counted, there are doubts that all could be housed. “I don’t know if we’ll ever get all of them,” said David Treadwell, a retired Army officer who fought in Vietnam and now directs Central Union Mission, an organization that cares for the homeless in the District. “You meet guys who are dedicated to being on the street.”

“Field experience shows everyone can be housed,” said Culhane. “Not without relapse, but it can be done.”

The VA’s 2012 budget includes $939 million to prevent and reduce homelessness, an increase of 17.5 percent from 2011.

And the demand for services continues to rise. At the VA Medical Center in Washington, the number of homeless veterans seeking treatment annually has grown from 900 to 2,000 during the past three years. The hallways bustle with veterans visiting doctors or attending substance-abuse programs and other classes.

Ending veteran homelessness seemed far-fetched to staffers at the center when it was announced in 2009. “It felt overwhelming at the time,” said Maria Llorente, chief of mental health services. But the housing vouchers and better coordination between Veterans Affairs and other agencies have made the goal attainable, she added. “We are genuinely optimistic.”

Eddie Baker, a 56-year-old Army veteran, works at the VA hospital providing peer support for homeless veterans, including more from Iraq and Afghanistan. “I can relate intimately,” said Baker, who has been homeless since 2004. “They understand that we’ve been through this.”

Baker, who lives at a homeless shelter in Capitol Heights, has tried to get a housing voucher, so far without luck.