New York ? All of 27, Jennifer Capriati counts as a veteran on the WTA Tour, a member of the old guard fending off the kids.

She’s had highs and lows, in tennis and away from it. The rapid rise as a teen phenom. The well-documented fall from grace. The remarkable return to the top, replete with three Grand Slam tournament titles and a brief stay at No. 1.

Through it all, Capriati always has been able to count on her power with a racket. The shots and smiles came quite easily Thursday night at the U.S. Open, where she reached the third round by overpowering Martina Sucha of Slovakia, 6-1, 6-1.

The tennis court is “where I live basically. I mean, I still get nerves, of course, playing in front of huge crowds, certain things might make me lose my focus,” the No. 6-seeded Capriati said. “But I don’t think you can get any more comfortable than how I feel about tennis tournaments.”

Mary Pierce also knows the ups and downs of pro tennis.

She’s been a major champion — twice. She’s also gone three years without a title at any level. She’s been ranked No. 3 in the world. And, waylaid by a long series of injuries, she’s fallen out of the top 100.

Faced with a 5-1 third-set deficit against No. 22-seeded Jelena Dokic, Pierce mustered just enough oomph and gumption to pull out a 6-2, 6-7 (5), 7-6 (5) victory and reach the third round on a day with a tournament-record total attendance of 56,183.

“I’m still not back to the level where I want to be. It’s still a process for me,” the 28-year-old Pierce said. “The fitness and my physical level are getting better, but it’s not there yet. My legs kind of weren’t there in the third set, so I just said, ‘Start going for your shots.'”

Andre Agassi always goes for his shots, conducting points as though there were a baton in his hand, and Thursday night was no different. Agassi, at 33 the oldest No. 1-ranked player in ATP Tour history, was challenged early by Andreas Vinciguerra but put together a tidy 7-6 (1), 6-1, 6-4 victory.

Agassi next faces two-time major champion Yevgeny Kafelnikov.

Jennifer Capriati returns a shot to Martina Sucha. Capriati won, 6-1, 6-1, at the U.S. Open Thursday night in New York.

The only games Capriati lost, curiously, were on her own serve, and she helped Sucha by double-faulting five times. Sucha might very well have just been happy to be there, having picked up a last-minute sponsor when it was announced she’d be playing at night in a nationally televised match. Sucha wore a patch for a doughnut company, hastily stitched on her shirt.

“I miss being at the top and playing good tennis,” said Capriati, who sipped a beer on court after winning a tuneup event last week for her first title since the 2002 Australian Open. “A lot of it is being physically fit. When I’m not, I’m missing some of my confidence.”

Capriati was in control throughout, whipping deep strokes to compile a 28-4 edge in winners.

According to Dokic, no one hits the ball harder than Pierce. Not Serena Williams. Not Kim Clijsters.

“Some of the shots she hit,” Dokic said, “I didn’t see.”

That might have been how Todd Martin felt as he tried to deal with French Open runner-up Martin Verkerk’s serves, which consistently topped 130 mph. But Martin, the 1999 U.S. Open runner-up, withstood the Dutchman’s 26 aces — which were counterbalanced by 12 double-faults — and eliminated No. 16 Verkerk, 6-3, 6-4, 6-7 (5), 7-6 (9).

Dokic and Verkerk were among a sizable group of lower-seeded players exiting in second-round action Thursday, including No. 24 Mardy Fish, knocked off by Karol Kucera, 6-4, 7-6 (7), 6-4.

No. 23 Wayne Ferreira was sent packing by American Robby Ginepri, who lost to Andy Roddick in the 2000 junior Open final. Ginepri advanced to the third round of a major for the first time by beating Ferreira, 6-2, 6-4, 6-7 (0), 6-2.

Seeded players advancing included major title owners Justine Henin-Hardenne, Lleyton Hewitt and Juan Carlos Ferrero.

Capriati was only 14 when she first made a Grand Slam semifinal, at the 1990 French Open. But she didn’t win a major until 2001.

Her problems in between are a reason the WTA Tour has its current age-eligibility rules to limit the number of tournaments players aged 14-to-17 can enter.

“Where did the time go? I don’t feel 27,” Capriati said. “I’m just going to keep going as long as I love it, and my heart is in it.”