Taisha Cobbs, Rachael Shane and the rest of the cheerleading squad at Alexandria's T.C. Williams High School were frustrated. Although it was time to practice their routines, they weren't allowed to do any of their flips or stunts -- because they might hit their heads on the ceiling of the school lobby.

"We need more room. We can't stunt out here because the ceiling is too low," said Taisha, 15, as the girls made do with stretches and cartwheels on the carpet. "We shouldn't have to practice in the lobby." Or the cafeteria or the auditorium, as often happens when the gym is overbooked.

Shifting cheerleading practices is one of many accommodations students and staff have made over the years to deal with chronic crowding at Alexandria's only public high school. On Thursday, the city's School Board is scheduled to pick a site for a new, $75 million T.C. Williams, and the likely choice is property it controls next to the school, which eventually will be razed.

"There is no other land that isn't allocated for something else or already purchased," board member Sally Ann Baynard said.

In Washington's burgeoning outer counties, lessening school crowding is a matter of buying more land and building new schools -- not cheap, not easy, but straightforward. In Alexandria and other older suburbs, there is precious little land left to buy, and what there is is expensive.

In Loudoun County, which is opening at least three schools a year for its rapidly growing population, sites often are provided by developers seeking approval to build subdivisions. But even there, school officials say, land can be hard to find. They are looking now, four years ahead of the usual schedule, for sites for an elementary school that will not open until at least 2009 and middle and high schools that will not open until at least 2010.

Alexandria's only alternative to the property next to T.C. Williams -- land now used for parking -- was nearby Chinquapin Park, which residents did not want to lose for a high school.

Parents are eager for the debate to end and the construction to begin.

The current high school was built in 1965 for 1,750 students and now has 2,110 -- a higher rate of growth than the city itself experienced during the same period. School officials looked into renovating the school, but consultants said that would cost nearly as much as building a larger one.

"We have to have an up-to-date high school for the people living here now and for attracting people who want to live in the Washington area," said parent Peter Coppelman, chairman of the Parent Teacher Student Association building committee.

"This is a starting point, but one with a tremendous amount of work behind it," School Board Chairman Mark Eaton said. "Now, we're telling the staff, 'Go . . . build a 420,000-square-foot educational space with a modern educational design that would be consistent with a high school for the 21st century.' "

In addition to the school, plans to build a two-story parking garage on King Street and a pedestrian bridge connecting the school stadium and the Chinquapin recreation center will also be considered. But plans could change as the architects proceed.

"There will be all sorts of unpredictable issues," board member V. Rodger Digilio said.

Longtime Principal John Porter said the school's design would be based "on how we want to educate our students. . . . This is the building that will serve the community for the next 40 or 50 years."

John D. Johnson, assistant superintendent for Alexandria schools, said Mosely Architects, a Richmond-based firm that has designed many other Virginia schools, will be asked to create a modern building with lots of windows and accommodations for future technological advances such as laptops on a wireless network.

Designers also will be asked to include flexible space to allow for smaller "schools within the school" so that, despite the size, students will "feel like it's a neighborhood school," Johnson said.

The staff plans to seek input from teachers, students and parents and is to propose a new educational program by May to guide the architects. German teacher Adam Levine has his wish list in hand, and it's long. First is space, "lots of it," he said wistfully. "That would be really nice."

Levine now teaches in a cozy but cramped room where every inch of floor and wall space seems to be in use. When students break into groups to practice their German, they must use the hallway.

Levine would like enough room to accommodate big, round tables where students could easily talk to each other. And he longs for a ceiling-mounted TV and VCR. Now, his television sits on an imposing eight-foot-tall rack; and his slide projector, on a cart at the front of the classroom, must be unplugged and the cord rolled up after each class so that no one trips over it.

Each classroom is supposed to have two computers, but Levine's has space for only one. And he would like to replace the blackboards and chalk with whiteboards and washable markers.

"I don't want to have to deal with this anymore," he said, holding up a chalk-saturated sponge that emits a small cloud of dust when he squeezes it.

The scheduled opening of a new T.C. Williams is four years and a lot of effort away.

"It's a huge undertaking," board member Linda D. Cheatham said, "but when you only have one high school, you have to do it right."