As if the reputation of Stuyvesant High School — often called the “crown jewel” of New York City’s school system — were not already shiny enough, a new book by a Washington Post reporter and Stuyvesant alumnus has arrived to burnish it.

In “A Class Apart: Prodigies, Pressure, and Passion Inside One of America’s Best High Schools,” Alec Klein recounts the mundane events of spring semester 2006 — the Sing! competition, Student Union elections, the SAT, college acceptances — through the eyes of a handful of students and teachers at New York’s most selective public high school. One student, the daughter of Ukrainian immigrants, worries about her parents’ response to a tiny drop in her grade point average. A football star and math whiz daydreams about his likely acceptance to Harvard. Charismatic and devoted teachers challenge their star students and try to save their troubled ones.

While Mr. Klein addresses some of the common criticisms of Stuyvesant, such as the extremely small number of African-American and Hispanic students, overall he takes for granted the school’s reputation for academic excellence. But comments from former teachers and administrators, recent graduates, and education experts offer a picture that is somewhat more complicated. While few question that Stuyvesant attracts a very high-achieving group of students, how well the school serves these students while they’re there is open for debate. Even the teacher who is Mr. Klein’s protagonist and hero, the math department chairman, Daniel Jaye, who in the course of the book makes a painful decision to leave Stuyvesant after 35 years to become the principal of a magnet school in New Jersey, suggested in an interview that Stuyvesant is overrated. “Stuyvesant has gotten very complacent in [its] status as the number-one school” in New York, he told the Sun, explaining he doesn’t see the administration aggressively pursuing new initiatives, such as partnerships with other schools, that would benefit the students.

He said that his current school, Bergen County Academies, “offers a lot more to students” than Stuyvesant does.

Stuyvesant, of course, has the reputation it does for a reason. Out of the estimated 26,000 students who take the Specialized High School Admissions Test each year to get into the city’s eight exam high schools, roughly the top-scoring 3% are admitted to Stuyvesant –– making it, statistically, harder to get into Stuyvesant than Harvard. Stuyvesant students’ average SAT score is 2076, and one out of four seniors gets into an Ivy League college. Stuyvesant students are regularly semifinalists and finalists in the Intel Science Talent Search. The long list of distinguished alumni includes the Nobel Prize-winning economist Robert Fogel, the physicist Brian Greene, the political scientist Samuel Huntington, writers like Frank Conroy and Gary Shteyngart, and the actors Tim Robbins, Paul Reiser, and Lucy Liu.

But critics say that mediocre teachers and a passive administration make Stuyvesant inferior to some of the other exam schools. The author of “Breaking Free: Public School Lessons and the Imperative of School Choice,” and a parent of two Stuyvesant grads, Sol Stern, says the current principal, Stanley Teitel, “makes the trains run on time,” but “does nothing to advance what Stuyvesant is supposed to do: to nurture these really smart kids so that they produce something that’s added value in their education.”

Mr. Jaye, when asked his feelings about his former boss, said: “Stan allowed me to grow and to be aggressive and to forge partnerships with City College and NYU and Columbia and set up the CCNY Scholars Program and have a 600-member math team. I am very grateful for the room that he gave me to grow personally, and I think the reason the math department became a powerhouse is because there was no micromanagement.”

In a follow-up e-mail, Mr. Jaye said that his successor in the math department has maintained the partnerships he initiated. In some other respects, though, Stuyvesant has dropped off the national scene. For instance, Mr. Jaye wrote, Stuyvesant was a founding member of the National Consortium for Specialized Secondary Schools of Mathematics, Science and Technology, but it has not been represented in the last few years at NCSSSMST’s professional and student conferences, even while three of the city’s other exam schools — Bronx High School of Science, Brooklyn Technical High School, and the High School for Math, Science and Engineering at City College — have sent large delegations.

In “A Class Apart,” Mr. Klein makes Mr. Jaye a major character, highlighting his activism on behalf of his students, while consigning Mr. Teitel to the background of his story. Mr. Klein nowhere directly criticizes Mr. Teitel, who he says in the prologue did not ask “for any control over the book,” though Mr. Klein’s access to the school was at the principal’s discretion. But the author does refer to Mr. Teitel at one point as “[t]he accidental principal,” alluding to the fact that his candidacy was a long shot until one of his rivals for the job was accused of molesting a student and removed from the building in handcuffs.

In an interview, Mr. Klein said that Mr. Teitel has a more understated personality than Mr. Jaye, and that, as principal, he has many constituencies to answer to, including parents, the Alumni Association, the combination of parents and alumni who manage Stuyvesant’s endowment fund, and, of course, the New York City

Schools Chancellor, Joel Klein. “It’s the kind of school where there are a lot of strong voices coming from different factions,” the author, Mr. Klein, said. “The thing that impressed me the most about [Mr. Teitel] was his ability to restrain himself from controlling people. He let Danny Jaye do his thing, and he let Randi Damesek [an assistant principal and, essentially, disciplinarian] do her thing, and he let me roam the school.”

Through a New York City Department of Education spokeswoman, Mr. Teitel declined to be interviewed for this article.

Mr. Jaye and Mr. Stern each praised the leadership of Mr. Teitel’s predecessor, Jinx Perullo, who was principal for five years before resigning in 1999. In an interview, Ms. Perullo said she quit because she felt she wouldn’t be able to effect any further change at the school, given the resistance from some leaders of the faculty.

“In a school that doesn’t have many problems around which teachers have to rally,” she said, “there can be a tendency to be happy with the status quo and to not be introspective.” For her part, she added, “I felt that the school needed some introspection, especially given the new building” — in 1992, Stuyvesant moved to a $150 million new facility on Chambers Street — “and our new place in the world of technology.”

Among other problems, Ms. Perullo said, the teachers’ union in the school eliminated the two staff positions that had to do with coordinating technology. She also wanted to replace the grading system, on which students are graded on a scale of 100, with letter grades, which she thought would help to diminish the level of competition and anxiety over grades, since students couldn’t agonize over why they got a 95 instead of a 96. She wanted Stuyvesant to be able to offer courses in a non-traditional way, so that if, for example, the school didn’t have a teacher who could teach nuclear physics one year, it could instead bring in a professor two days a week to teach it after school. But despite the support of some like-minded members of the staff, Ms. Perullo found it impossible to make these changes.

In a review of “A Class Apart” on Amazon titled “Charming Read, Narrow View,” Anna Wiener, a 2005 graduate of Stuyvesant, wrote that not every student there is as brilliant as Mr. Klein suggests, nor “as caught up in the illusion of Stuyvesant as Klein himself gradually seems to become.” The quality of the teaching is highly variable, she said, with the best teachers generally assigned to the highest-level classes. “[S]tudents who are not in advanced-level classes have a higher probability of being taught by a teacher who is less experienced, less engaging, or simply egregious at their job.” Ms. Wiener, who has matriculated at Wesleyan University, responded to a message sent via Facebook, confirming that she wrote the review but declining to answer further questions.

Ms. Perullo described Stuyvesant as “a big impersonal place,” where kids can get lost. Some alumni, however, describe the anonymity as part of the school’s appeal. James Carmichael, who graduated in 1997, transferred to Stuyvesant from Fieldston because he felt the private school environment was too cushioned. But Stuyvesant “sounded perfect for me.”

Stuyvesant was a big machine, he said, but a fair one. “It wasn’t like the soft skills thing of a private school, where you learn to finesse people. At Stuyvesant, you show up, and you study really hard for the tests,” he said, “and your grade is dependent on [them]. That was kind of the rule for everybody.”