NEW YORK » Catholic schools have been bleeding enrollment and money for years, and many have been forced to close. But some, like St. Stephen of Hungary, on the Upper East Side of Manhattan, have found a way to thrive — attracting a more affluent clientele by offering services and classes more commonly found in expensive private schools.

Selling points include small class sizes and extracurriculars beginning in the youngest grades. And by often charging far less, these schools have been able to stabilize themselves and even grow.

"Our competition or our standard isn’t another good Catholic school," said the Rev. Angelo Gambatese, the pastor at St. Stephen of Hungary church, which shares a building with the school. "It’s the best independent schools in Manhattan, and we intend to achieve the same level of performance that they do, academically, developmentally."

If the neighborhood has welcomed a nurturing school that comes without sticker shock — tuition at St. Stephen starts at less than $8,000, less than a quarter of what some Manhattan schools charge — school leaders acknowledge that there has been a cost. Three years ago, 46 percent of the students received free or reduced lunch, in keeping with the Catholic Church’s mission of tending to the poorest; this year the number is down to 17 percent.

Enrollment of African-American students has dropped 15 percent, Hispanic students have dropped 33 percent and the school, which runs through the eighth grade, is noticeably whiter in its lower grades.

Patrick J. McCloskey, director of Funding Solutions for Catholic Schools, an initiative at Loyola University Chicago, said it was not unusual for schools to try to appeal to neighborhood families, since most of them are strongly tied to their parishes. "But educating the poor is part of the Catholic mission as well," he said.

In some states, Catholic schools have benefited from expansions of voucher programs that allow some students, usually those in poor neighborhoods, to attend private school at public expense. But other schools have taken the approach of St. Stephen, by reinventing themselves with new features to bring higher-income students into the fold. St. Therese Catholic School in Seattle received financing from the Bill and Melinda Gates Foundation and Seton Partners, a San Francisco-based nonprofit, to convert itself into St. Therese Academy, a blended technology school. This fall, computers will be in every classroom to enable small-group learning, said Scott Hamilton, managing director of Seton Partners. Enrollment is expected to reach 185, up from 95.

In Tacoma, Wash., Holy Rosary, a struggling Catholic school, has converted itself into a dual language Spanish immersion program, in part to attract more affluent families. Enrollment is expected to be 150, up from 100.

Dr. Thomas McNiff, superintendent of schools for the Archdiocese of New York, where 46 schools have been shuttered since 2006, praised the turnaround of St. Stephen, which was once designated for closure.

"We are here to serve children," he said. "We are not looking to see their ethnicity or their socioeconomic background."

He said that 64 percent of students in New York City Catholic schools lived at or below the poverty line. The Upper East Side, where St. Stephen is, is predominantly white, he added.

The schools have also had to be careful not to jeopardize their Catholic identity, to avoid alienating their traditional core. At St. Stephen, crucifixes are in every classroom, there are morning prayers every day, and religion seems to be the one subject whose curriculum is relatively unchanged.

St. Stephen was founded in 1928, serving working class families from the neighborhood’s Hungarian community at a cost of 50 cents a month. The nuns slept where the 4-year olds now eat their veggie chips.

While 70 percent of the students are Catholic, a figure that has not changed, it has a more Franciscan focus on kindness and respect rather than papal edicts, which makes it more palatable to families not traditionally in the Catholic school market.

"I don’t feel like it’s holy rollers over there," said Richard Sher, a parent of two at the school who is half Jewish, half Protestant. Mass is every other week and the homily is more of a discussion, than a lesson. When Gambatese talked in May to the youngest students at Mass about Adam, he wondered why Adam asked God for more humans. "He wanted people to talk to and play with," said Sabrina Vidal, age 8. "Yes!" said Gambatese . "Don’t you get tired of hugging a lion?"

St. Stephen offers the kind of extras found at far more expensive schools, like French for 3-year-olds, violin for fourth- and fifth-graders, iPads for sixth- to eighth-graders. But some parents, Catholic and non-Catholic, said they were also drawn to the discipline and values-based approach at St. Stephen, elements that have fallen out of fashion at most nonreligious schools. "We were looking for structure and that’s what we got," said Deirdre O’Connell, a parent who works in banking.

In Katherine Peck, the entrepreneurial 33-year-old at the heart of St. Stephen’s revitalization, they also got a principal schooled in progressive teaching. Classrooms are no longer teacher-focused, with students at desks, but student-centered with children at tables. Students have publishing parties every month to showcase their writing, textbooks have been de-emphasized in favor of hands-on learning and every classroom has an interactive projection system.

Peck, who is Catholic and attended Teachers College of Columbia University, said Catholic schools gave her more flexibility than the public schools where she had taught. (She also taught at the Epiphany School before coming to St. Stephen.) "Everything I was doing at Teachers College, I could do in the classroom," she said, compared with the public school where she said everyone was required to teach from the same page.

Peck, dressed in pearls and Tory Burch shoes, and sitting in front of a portrait of Pope John Paul II, said she had to save the school by rebranding it to families who could afford the tuition and who will invest in the school.

"We struggle to keep diversity as the school is changing," she said, adding that stabilizing the school was her primary focus in her first years.

Those efforts have paid off. There are now 13 full-time teachers, up from 11, thanks to newfound success in fundraising.

The school’s annual fund raised $2,000 three years ago; this year about $120,000 has been pledged. The spring auction raised $60,000, up from $20,000 two years ago. A golf fundraiser in Pelham this spring, raised $10,000. And when the school made a plea for money for six new iPads a few weeks ago, grandparents donated enough for nine. This summer a $250,000 science lab will be completed.

"Kate Peck is like a gem," said O’Connell. "When she’s done with all this not-for-profit stuff, I keep telling her she should come to Wall Street."