The deadline passed more than eight months ago and still the phone calls roll in: How can I get my child into the Thomas Jefferson High School for Science and Technology this fall?

For the fourth time that morning and probably the thousandth time since the deadline last Dec. 1, Dianne Hardbower, the admissions office secretary, had to give the disappointing news. "I'm sorry, we don't have any openings," she said. "We're becoming too popular, I guess."

Five years after Fairfax launched the math-and-science magnet school in Annandale, Jefferson has become a victim of its own success.

With virtually unparalleled technological resources for a public high school and a string of high-profile academic achievements, Jefferson has secured an undisputed reputation as the premier high school in Northern Virginia and one of the best in the nation.

As word spreads, the clamor to get in has grown sharply, according to school officials. Applications have more than doubled for the same number of slots, and each year the school turns away scores of qualified applicants. Some officials expect that pressure from frustrated parents will build in the near future.

"The application pool in general has just exploded on us," said Geoffrey A. Jones, the Jefferson principal. "We clearly are in the unfortunate position of turning away very gifted students, students who would be successful here at the school. And that's been increasing in the last two years."

In the fall of 1986, 814 youngsters applied for 400 positions. Last fall, there were 1,615 competing to enter. When two students dropped out last year, the school received 88 applications to fill their slots.

In addition to the 400 accepted for next year, Jones said, 150 to 180 who were not accepted were considered qualified; there simply wasn't room for them.

"It just makes sense that this would be a problem that would be exacerbated as each year passes," said Susan Provyn, president of the Fairfax County Association for the Gifted. "It's just getting highly competitive."

"I wish we had enough Thomas Jeffersons that we could let them all in," said Jack Dreyfus, a TRW Systems executive and president of the Fairfax County Public School Education Foundation. "That's a nice dilemma to have. It's better than the other way around."

Several rejected applicants said they were disappointed, but noted that their parents were more upset than they were.

"My dad expected it of me, because my brother made it in," said Mark Stalzer, 14, who instead will attend Hayfield Secondary School. "He didn't get real mad. It was just one of those guilty looks: 'I think you could've done better.' "

Another unsuccessful applicant, Chris Bartus, 14, of Burke, said he will go to Bishop Ireton High School in Alexandria. "If it wasn't this," he said of Jefferson, "it was going to be a Catholic school."

Opened in 1985, Jefferson was designed to provide an intensive academic experience for gifted students from throughout Northern Virginia. With enthusiastic backing from the business community, the school created 11 laboratories in such areas as robotics, telecommunications and biotechnology.

The school's course catalogue reads like something from a well-endowed research university, with classes in genetics, plant tissue culture, computer architecture and artificial intelligence, as well as a wide array of languages, including Russian, Japanese, Korean and Chinese. Students have an eight-period day, compared with six or seven periods in the typical public high school, and per-pupil spending is $7,908, nearly $1,000 more than for regular high school students.

Jefferson's success stories have astounded the area's educators:

In a national competition, four students won the first supercomputer ever installed in any high school in the world.

Fifty-six of the 359 seniors who graduated in June were National Merit Scholar semifinalists, twice as many as any other Washington area school and fourth highest in the nation.

The average Jefferson student's Scholastic Aptitude Test score is 1,292, nearly 400 points higher than the national average.

Students who took Advanced Placement tests scored high enough to earn college credit on nearly 95 percent of the exams.

All but one graduate this year is going on to college, 32 of them to Ivy League schools and 93 of them to the University of Virginia.

To get into Jefferson, an eighth-grader must excel on an entrance examination, have impressive grades and provide teacher recommendations. For the first cut, the admissions staff bases 80 percent on the test and 20 percent on grades; thereafter, each student's application is read by 15 judges, according to admissions director Ann Greenwood.

Students from Fairfax, Prince William and Loudoun counties and Fairfax City, Falls Church and Manassas are eligible to attend at no cost; school districts in Alexandria, Arlington and Manassas Park have chosen not to send students to Jefferson.

Jefferson has tried to find ways to make its resources available to more students.

In June, it began offering summer classes to about 140 applicants who were not accepted to the regular school year, giving them the equivalent of the technology class they would have taken in freshman year had they been admitted. Four of the school's 11 specialized laboratories were kept open this summer for other students to use, and libraries and computer laboratories will be kept open until 6 p.m. twice a week during the regular year for non-Jefferson students.

For the moment, expansion of Jefferson's student body seems unfeasible; with nearly 1,700 students, the school building has already exceeded its listed capacity of 1,600, even after an extensive $6.4 million renovation.

Fairfax Superintendent Robert R. Spillane has talked for years about creating a new magnet school focusing on the arts and humanities. However, that idea has not progressed beyond the discussion stage and, given the current fiscal climate, may not be realistic.

School Board member Carla M. Yock (Mason District), whose daughter Torunn graduated from Jefferson in 1989, has drafted a memo calling for a scaled-down version of the same thing. Instead of designating a full school, she proposed starting four smaller humanities centers within existing county high schools.

Fellow board member Joanne T. Field (Dranesville), whose district includes McLean, home of many frustrated applicants, suggested outfitting a mobile classroom-trailer with some of the sophisticated Jefferson equipment and parking it at different high schools for a month or more at a time.

While these ideas languish, some expect to see parental pressure in coming years to close Jefferson to students from outside Fairfax; more than 15 percent of the students now come from other jurisdictions, mostly from Prince William.

To do so, Jefferson would have to sacrifice $700,000 in state funding and $1.6 million in tuition payments from other jurisdictions annually, out of an overall $10.1 million budget.

Marlene Blum, whose son, Matthew, will be a senior at Jefferson, said she does not favor the idea, advising disgruntled parents to work to improve gifted programs in their base schools.