Greenwich, Conn. ? Three boys are sprawled out on the classroom floor, their heads resting on their backpacks. Nap time in kindergarten? No, a meeting of the Power Nap Club at Greenwich High School in this wealthy community of high achievers.

The club was started by a teacher who figured that with all the pressure to succeed, some teenagers could use a little you-time.

Once considered a joke, the Power Nap Club has grown to about 20 members who meet on Mondays after school. The club even has T-shirts, a logo of a cardinal (the school mascot) wearing a nightcap, and a Latin motto: “Veni vidi dormivi I came, I saw, I slept.”

At meetings of the Power Nap Club, members are encouraged to nod off in the classroom, and there’s no making fun of those who snore.

In Greenwich, one of America’s richest communities, with lots of lawyers, doctors and investment bankers, students are expected to get top scores on the SATs and apply early to Ivy League colleges. Extracurricular activities such as sports are a must to enhance the resume.

“You have to be the best athletically, intellectually, wear the best clothing, go to the best schools,” said Anton Anderson, a 58-year-old English teacher who started the club in 1998. “I think they buy into it. But it also means their lives are difficult and they need a little time for themselves.”

Thomas Murphy, spokesman for the Connecticut Education Department, said he is not aware of any other nap clubs in schools.

“But that doesn’t mean it is not an area to explore,” Murphy said, wistfully recalling nap time when he was a child. “As a 51-year-old male, I believe naps have been very underrated in this world.”

Jenna Goldstein, left, a student and co-president of the Power Nap Club, and English teacher Anton Anderson set up an audio tape at Greenwich High School at the start of Power Nap Club, while other students and teachers close their eyes, put their heads down on a desk or lie down for a nap. The Power Nap Club, started by Anderson in 1998, has grown to about 20 members who meet after school on Mondays.

At 2,450-student Greenwich High, the Power Nap Club began to grow in popularity about two years ago when students Jenna Goldstein and Kelly Hannigan became enthusiastic supporters.

Goldstein and Hannigan, now seniors and co-presidents of the club, laughed at the idea at first. But they said they gradually came to appreciate the club, which also teaches relaxation techniques, for helping them manage their busy lives and focus better.

In Greenwich, “you have to do everything perfectly,” said Goldstein, who plays varsity basketball, works with two autistic children and has a job as a party planner.

Those expectations fade for a fleeting few moments on Mondays, when students and teachers take a 20-minute nap.

Brian Mok, 17, said the club has taught him to take quick, refreshing naps rather than long snoozes. That has helped him avoid such embarrassing incidents as the time his history teacher caught him sleeping in the back of the class.

“The teacher was like, ‘Everyone look at Brian in the back.’ I heard laughing and I woke up,” Mok said.