SAN JOSE — A little girl stood before the council in a purple T-shirt and told the city’s elected leaders she had slept in a cardboard box under a highway overpass, while fretful homeowners clutched yellow signs complaining that San Jose already does more than its neighbors to help the homeless.

In the end, after a 15-hour meeting that stretched past 2 a.m. Wednesday, the City Council made plodding progress on a host of proposals aimed at easing one of San Jose’s most intractable problems at a time when Silicon Valley’s soaring technology economy is widening the gulf between rich and poor.

The council on an 8-1 vote upheld a 162-unit apartment complex at 2500 Senter Road for chronically homeless residents, denying an appeal from opponents who threatened to sue San Jose over potential loss to their home values.

The council also approved setting aside $5 million for a program that provides funding for capital improvements to landlords who accept referrals to house homeless veterans. And the council unanimously extended a policy that allows churches to house homeless people without permits for another year. City leaders agreed to expand the program to allow up to 30 people to stay in one location for 90 days.

But the council in a unanimous vote backed away from approving a project that would have allowed temporary modular homes for up to 102 homeless people for 15 years on a six-acre Evans Lane site in Willow Glen, voting instead to study using it for a larger permanent housing project. And the council passed on a proposal to sanction a supervised tent campground, with city officials saying they weren’t successful in finding a suitable operator or a site for an encampment.

“I think we made progress Tuesday night,” said Jennifer Loving, executive director of Destination: Home, a nonprofit that works to end homelessness. “We’ve never had a group of more committed local elected leaders earnestly looking at solving this problem. But we still have a lot of fear that solutions to homelessness will look like the problems of homelessness. The real work we have ahead of us is to remove the fear.”

Loving said if San Jose is serious about ending homelessness, then “we are going to have lots of tough conversations in the future about new projects and where homeless people will live.”

The most contentious of the proposals was the Senter Road project, with Councilman Tam Nguyen, whose district includes the project site, casting the dissenting vote. Councilmen Manh Nguyen and Johnny Khamis were absent.

Nguyen echoed concerns from residents who said the project was “rushed” with little outreach, the site is too close to neighbors and could increase crime and blight in the area.

“Common sense tells us this will end in disaster,” said nearby homeowner Jonathan Fleming. “They will drink, do drugs and roam our streets.”

But the project, which will be built on county-owned land at no cost to San Jose, includes a dozen on-site employees, 24-hour security and access to counseling and health services. Advocates for the homeless say permanent supportive housing could actually reduce crime and 84 percent of people placed in projects like Senter Road stay housed. The city’s Planning Commission gave its unanimous approval in April.

“We have a good operator, we have good amenities and we can make this a benefit to the community,” said Councilman Raul Peralez. “We have a good project.”

Vice Mayor Rose Herrera encouraged the project managers to regularly meet with neighbors to discuss concerns — one of Nguyen’s ideas — and asked that more city services and police resources be dedicated to neighborhoods that house the poor.

Though Tam Nguyen opposed the Senter Road project, he urged the council to give legal tent cities a chance. He slept in one in Portland earlier this year and said it could work in San Jose. But Mayor Sam Liccardo said the city would better serve the homeless with other ideas.

“It seems to me we should focus our energies on all the other initiatives we have,” said Liccardo, adding that council members pushing the idea should find sites in their districts.

With the Evans Lane modular home proposal, Councilman Pierluigi Oliverio, who represents the district, convinced his colleagues to study other housing options. The city’s housing staff will bring alternative options to a council meeting on Aug. 16.

“There’s been one concept floated and there have been deep concerns,” Oliverio said.

Despite the unanimous approval, some city leaders said the move sends “mixed messages” to residents. Under increasing public pressure, the council over the past year has pushed for quick solutions to house homeless people — yet they put off a project that could be ready in about a year to study longer-term alternatives.

The program that allows churches to house homeless people without permits transformed Yolanda Estrada’s life. The 50-year-old had been homeless for three years before she started sleeping inside three South Bay churches this year. Now she’s on her way to moving into an apartment.

“My self-esteem was raised up and these people genuinely care about me,” Estrada said. “I felt a sense of belonging.”

Contact Ramona Giwargis at 408-920-5705. Follow her at Twitter.com/ramonagiwargis.