The National Child Research Center is a well-established private preschool whose tuition compares to that at some public universities. It is nestled among million-dollar homes on a narrow two-way street with a blind curve in Cleveland Park. With its white columns and wraparound porch, the three-story school looks very much like the residence it was 75 years ago. And that's the way many of the NCRC's neighbors want it to remain.

But if Susan Piggott, the school's director, has her way, the NCRC could change a great deal. In November 2002, NCRC asked the Board of Zoning Adjustment to permit an increase in the number of enrolled students to 185 and to almost double in size, from 9,500 to 18,000 square feet. Neighbors, some of whom have sent their children to the NCRC, were not pleased.

The continuing battle between the NCRC and its neighbors is similar to what has happened in many communities in Northwest Washington as wealthier and younger families have moved in and increased demand for school services. Over the last five years, at least a dozen private schools in the District have sought either to expand their facilities or to increase their enrollment. Washington International School, for example, wants to add a library and classroom building and St. Albans wants to enlarge its athletic fields. Yet some of these elite schools have run up against the same kind of "not in my back yard" opposition that community groups often direct at dance halls.

Neighbors complain about traffic, noise, unenforced parking regulations and broken agreements. The complaints are not new. Three years ago council member Kathy Patterson (D-Ward 3) convened a task force to look at the impact of private school expansion on surrounding neighborhoods. The 13-member task force made up of Ward 3 residents offered eight recommendations. They included establishing a zoning resource center to help mediate disputes, having school facilities remain open to the community after hours and requiring schools to adopt a code of conduct that would help them be good neighbors on issues like parking and traffic flow.

"The task force recommendations, and the process of private school and neighborhood leaders talking together, helped lower the decibel level and also gave some concrete steps to take," Patterson said.

In response to the task force, the Association of Independent Schools of Greater Washington and the National Association of Independent Schools issued a Good Neighbor Guidebook in May 2004.

For their part, schools like the NCRC and Woodley Park's Aidan Montessori have tried to address community concerns through such measures as traffic management plans -- staggered systems of dropoffs and pickups that resemble the arrival/departure system at an airport.

Yet, as at the airport, the system doesn't always function as planned. As he walked around the NCRC's playground, Bruce Beckner, an Advisory Neighborhood Commission 3C member and one of the NCRC's direct neighbors, said the school's parents can be late and impatient. Rather than waiting in line when picking up their children, he says, they sometimes jump ahead and clog Highland Avenue. With increased enrollment, the congestion and noise will only grow, neighbors argued.

In March, the Board of Zoning Adjustment denied the NCRC's application to increase enrollment. The school's bid to expand is now in the D.C. Court of Appeals. This fall the school will enroll 171 students -- 51 more than their enrollment cap allows.

Piggott expressed confidence about the eventual outcome.

"We have no plans to reduce our enrollment or to move away from this site," she said. "It's been here forever and it needs to be here forever."

Beckner suggested that neighbors might be willing to negotiate enrollment terms if the proposed expansion is put aside.

"There's no sentiment that people want the school to leave," he said. "There are physical limitations that limit what it could be. You can't get a size ten foot in a size five shoe." Beckner also said the NCRC might want to consider a satellite campus, an idea that Aidan Montessori recently has been forced into accepting.

Aidan Montessori, a pre-K and elementary school, is in a unique position. In 1995, when it moved to Woodley Park, the school signed a three-party agreement with the Woodley Park Community Association and ANC 3C. Terms of that agreement stipulated that Aidan would seek an enrollment cap of 180 through the Board of Zoning Adjustment. But Aidan, due to an administrative oversight, never requested the cap. So in 2002, when the school went to the community association to discuss plans for a possible rooftop playground and classroom, the community balked at the proposed expansion, citing the broken 1995 agreement. To complicate matters, Kathy Minardi, the school's director, said, they accepted 210 students in the spring of 2004.

A sizable number of Woodley Park residents supported Aidan. Among them was James Millward, who sends his two daughters to the school.

"Many, many parents around here are putting their kids in Aidan, and it's nice," Millward said. "It's a neighborhood school; it's within walking distance."

Aidan and ANC 3C are working on a plan to reduce enrollment to 180 students for the fall of 2007. If Aidan does not comply, the school will have to donate money to a charity of ANC 3C's choosing, in an amount based on a formula that includes Aidan's tuition rates and how many students are over the cap.

"They have decided to make an issue out of Aidan, and it's been very strong and ardent," Minardi said. "Their fervor in choosing to work in a compliance-oriented fashion is partly an example to other independent schools. Unfortunately, we're the little guys, so it's a hardship for us." Aidan is now looking to relocate its elementary school to another site. The preschool will remain in Woodley Park.

ANC 3C is also playing hardball with St. Albans, the all-boys school on the grounds of the Washington National Cathedral.

The ANC has opposed the school's application to, among other things, build a partially underground auditorium and expand athletic fields. The existing traffic and parking problems caused by use beyond the school day concern many neighbors. More extensive facilities -- without firmly established and enforced ground rules -- only compound the problem, they say.

"There is a real balance that you try to establish between the schools and the community, and we try not to restrict school programs, but some of the programs are pretty extensive," said Nancy MacWood, the ANC 3C chairwoman. "A neighborhood may be faced with very little respite. The peace and quiet is seriously endangered with that amount of use."

St. Albans's director of communications, David J. Baker, said he would not comment on the situation because negotiations with the zoning board and ANC 3C are ongoing.

If the agreement between ANC 3C and St. Albans is anything like the agreement the commission reached with the Washington International School, then St. Albans can expect the support of ANC 3C only if it meets certain conditions. But the negotiations between Washington International and the ANC produced a compromise that perhaps could be a model for resolving other disputes.

When Washington International proposed a 28,000-square-foot expansion at its Cleveland Park location, the school entered into a three-part agreement with an ANC 3C commissioner and an historic preservation group to outline the terms of the expansion. The agreement sets limits on the number of non-athletic evening programs and noise-producing events the school can have each year. The Board of Zoning Adjustment approved the school's application in May.

"They were very sensitive to the concerns of the neighbors," said MacWood about Washington International. "They restricted their outside use and have been very responsive."

Richard Hall, head of Washington International School, said the experience has been positive. "We had eight meetings. We talked about issues of historic preservation and traffic. Everybody went into it with the feeling that we wanted to get something accomplished and respond to everybody's concerns."

Susan Piggott, head of the National Child Research Center, is awaiting a decision by the D.C. Court of Appeals on a proposal to increase the school's enrollment and faculty. Some neighbors worry about noise and parking, concerns common in areas where schools are contemplating expansion.