JOHN CARLOS FREY:56-year old Lendell Seay proudly shows off his tidy one bedroom apartment, which overlooks the 5 Freeway in East Los Angeles.

The unit's bathroom is so big he keeps his bike in it, and there's plenty of room for his collection of hats, many of which tout his military service.

LENDELL SEAY: My primary job was in motor T, transportation.

JOHN CARLOS FREY:Seay served in the Marines for more than 21 years, including Desert Storm in Iraq, before retiring in 1998. But despite his successful military career, after his fiance passed away from a stroke in 2004, Seay found himself in a downward spiral.

LENDELL SEAY: And that's when the drinking and everything really, really kicked in.

JOHN CARLOS FREY:For you?

LENDELL SEAY: Yes, and I just — just fell apart and lost everything.

JOHN CARLOS FREY:So you found yourself where?

LENDELL SEAY: I found myself in the — in the streets around Culver City and Santa Monica.

JOHN CARLOS FREY:From one day to the next, you were homeless?

LENDELL SEAY: Yes.

JOHN CARLOS FREY:Before he moved into this apartment last October, Seay had been homeless, off and on, for a decade.

LENDELL SEAY: Everything that I made was mostly spent drinking.

JOHN CARLOS FREY:Famously sunny Los Angeles has long been known as the homeless capital of America, from beachy communities like Santa Monica and Venice to Skid Row downtown. There are about 45,000 homeless people in L.A. county, about 4,000 of whom are veterans.

The number of homeless vets in the city of L.A. has fallen by about one third since 2009. And last year the city joined an ambitious national effort already underway to completely end veteran homelessness by the end of this year.

L.A.'s commitment coincided with an event last July attended by First Lady Michelle Obama, who has championed veterans initiatives for the Obama administration.

MICHELLE OBAMA: And make no mistake it is an aggressive goal. but we have seen time and time again that if you break these numbers down then this problem becomes eminently solvable.

MAYOR GARCETTI: I don't think anybody's had the confidence that we'd ever be able to make a dent in homelessness. We've just come to accept that we manage homelessness, that we try to make it less bad, but we never make it better.

JOHN CARLOS FREY:Los Angeles Mayor Eric Garcetti is a former Navy Reservist himself. He says the city's effort to end homelessness among veterans is different than how things used to be in L.A.

MAYOR ERIC GARCETTI:Our policy was very lazy. “I just do housing,” “I just feed them,” “I'm a free health clinic,” and it — and it admirably — dealt with the crisis of people potentially dying on our streets, but it never turned their lives around permanently. That's what's changed now.

JOHN CARLOS FREY:The first step of this new model is a permanent house, funded mostly at government expense with services then added around the resident. It's called permanent supportive housing. And that's what Lendell Seay found himself in.

Seay lives in this complex that houses only formerly homeless veterans. While there is no firm program that he has to follow, he has access to support services, including onsite case managers, mental health counseling, substance abuse treatment, and even a community garden.

Officials in L.A. point to research showing nearly 90 percent of chronically homeless people remained housed after five years using this model.

For Seay, who has been sober for more than two years, it's more than he had hoped for.

LENDELL SEAY: It feel good. Sometimes, I walk around the apartment and no TV or nothin' on and just singin' for no reason at all. And then I catch myself doin' it and I start to laugh and I say, “You must be goin' crazy now.” But I'm just happy, it feel —

JOHN CARLOS FREY:A good crazy.

LENDELL SEAY: It feel good.

JOHN CARLOS FREY:There is no time limit on staying in the apartment. Residents generally pay 30 percent of their income in rent. For Seay, that's $470 from his pension. The rest is subsidized with a federal voucher specifically for homeless veterans. Since 2008, nearly 80,000 of these vouchers for homeless vets have been awarded around the country.

CHRISTINE MARGIOTTA:I'll sign it, thanks.

JOHN CARLOS FREY:Christine Margiotta runs Home for Good for the United Way of Greater Los Angeles, which has coordinated the efforts of hundreds of service providers working to help homeless vets. She says housing for the homeless, including veterans, is less expensive than trying to care for people on the street, which costs nearly $1 billion annually in L.A.

CHRISTINE MARGIOTTA:Because that person is using the emergency rooms for their primary health care. They may be cycling in and out of jail or prison. They're really suffering, out on our streets. What we know is that permanent supportive housing is actually 40 percent cheaper than leaving someone on the streets and, in our minds, doing nothing

JOHN CARLOS FREY:But despite the progress made, there's no shortage of homeless people, including veterans, on the streets of Los Angeles.

Early one morning we went to Skid Row in downtown L.A. with outreach workers from U.S. Vets, a non-profit veteran support group. There we met Benjamin Barraza Jr.

JOHN CARLOS FREY:Can I ask you how long you've been on the streets?

BEN BARRAZA: How long? Right now, it's — it's — since I've been out of prison? Two years ago.

JOHN CARLOS FREY:You've been on the street for two years?

BEN BARRAZA: Yeah.

JOHN CARLOS FREY:Barraza is an Army veteran who served from 1971 to 1974. But he told us that he'd also spent time in prison. Since he'd been out, he'd been staying in Skid Row shelters. He showed us the few essential items that he keeps with him.

BEN BARRAZA: I got it all here, man. You know, this is my little kit, you know. you gotta keep clean, smell clean, you know.

JOHN CARLOS FREY:Despite qualifying for a Federal housing voucher, Barraza had not been able to find a permanent house. For him and many others on the street, finding an affordable apartment or placement in a facility with services isn't easy.

JOHN CARLOS FREY:Is it frustrating?

BEN BARRAZA: Oh man, it's — it's — it's — gives me, right now, I'm gettin' a headache right now, just thinking about it.

JOHN CARLOS FREY:All the things you have to deal with just to get a place.

BEN BARRAZA: Well, because I can't even get around. I mean, I'm obese. I put weight on, you know, when I was in prison my mother died on me.

JOHN CARLOS FREY:Wow, I'm so sorry.

BEN BARRAZA: You know, I caught hepatitis C.

JOHN CARLOS FREY:Even with the focus of the federal government and local officials on veteran homelessness, Barraza and thousands of other tough cases are still on LA streets.

JOHN CARLOS FREY:I was on the street this morning.

MAYOR ERIC GARCETTI:Uh-huh.

JOHN CARLOS FREY:And we ran into some veterans.

MAYOR ERIC GARCETTI:Yeah.

JOHN CARLOS FREY:From my eyes, it looks like an impossible task.

MAYOR ERIC GARCETTI:Yeah.

JOHN CARLOS FREY:These are people who are in dire straits. How do you deal with that population?

MAYOR ERIC GARCETTI:The more you go into the population, the tougher it is to achieve that goal. Because towards the end, it is the people who are the most service-resistant who most deeply experience mental health challenges when people have PTSD, substance abuse issues, which often intermingle with each other. Some will take more time, but I'm confident we can make sure that each one of them has a pathway off our streets.

JOHN CARLOS FREY:Some cities, including Phoenix, Salt Lake City, New Orleans, and Houston have said they've been able to house their entire populations of chronically homeless vets with permanent supportive housing. But for L.A., time is short if the city hopes to meet its year-end goal. And that arbitrary deadline has concerned some advocates.

Steve Peck is the CEO of U.S. Vets, which is a partner in the city's efforts and houses more than 1,000 veterans in the L.A. area.

STEVE PECK: My fear is that, you know, December 31st, someone's gonna plant the flag and say, “We've done it.” And anyone else then everyone diverts their attention to something else. We're gonna be doing this for years because there are gonna be veterans falling toward homelessness for years and years to come.

JOHN CARLOS FREY:Peck, a Marine veteran, also worries that putting so much focus on permanent supportive housing provided with almost no preconditions, an approach known as ‘Housing First', leaves many vets out, including those who may simply need some help getting back on their feet.

STEVE PECK: I think the trap that people get into is that they hear about something like Housing First and say, “That's the answer.” They focus on that as the one answer. And it's a very complex problem. All veterans are different. They all have different needs. We've discovered that here.

JOHN CARLOS FREY:There's also concern that the focus on homeless vets will come at the expense of the broader problem. In fact, overall homelessness in L.A. is up 12 percent since 2013 according to data released last month. And despite the attention and massive effort, the city of L.A. even saw a small increase in homeless vets.

JOHN CARLOS FREY:Los Angeles has had a reputation for having a very large homeless population.

MAYOR ERIC GARCETTI:Yeah.

JOHN CARLOS FREY:For decades. This is nothing new. So, it seems — I guess I'm being a skeptic here that you're going to be able to get to functional zero by the end of the year but this has never happened before.

MAYOR ERIC GARCETTI:It's never happened. But when I was campaigning for mayor I said, “I don't wanna just manage homelessness.” We needed to take a discrete population to give people the confidence that if we can end veterans' homelessness , we can attack chronic homelessness, families and other populations like foster youth, who each have distinct needs.

JOHN CARLOS FREY:For vets, the city will need systems in place. In the next three years, L.A. will have about 10,000 new veterans returning home and if the trend continues, hundreds will at some point be homeless.