And so Serena Williams’s comeback begins. Receiving a wild card into this year’s U.S. Open and winning a few rounds against mostly overmatched (or in the case of Ana Ivanovic, overly nervous) opponents was the easy part. Beating a fit and determined opponent like Amelie Mauresmo, that will take a lot more work.

Mauresmo again proved herself worthy of her no. 1 label last night, dispatching Williams with a combination of stamina and agility, and perhaps most important, a heavy dose of the confidence that helped her capture the Australian Open and Wimbledon this year.

Mauresmo ended her 6–4,0–6,6–2 victory with a flourish, charging a drop shot from three feet behind the baseline and then anticipating a forehand down the line from Williams. Mauresmo pounced and angled a backhand, cross-court volley over the net by a few inches. Off the court it rolled, and off went Williams.

Too often tennis matches are said to be defined by a single point or a single shot, as if all those other forehands and backhands did not play an equal part in a victory or a defeat. Last night, though, one rally — 35 strokes in all — explained the entire match.

Mauresmo led 3–2 when Williams served at 15–30. The 24-year-old former world no. 1, playing her best tennis since she won the Australian Open in 2005, had begun to tire. Her groundstrokes lacked the zip they had in the first two sets, and her footwork had become increasingly sloppy. Mauresmo sensed that she had nothing more to do than keep the ball in play. On the last stroke, the Frenchwoman hit a ball deep to Williams’s backhand, and Williams could not position her feet properly. Her down-the-line attempt found the net.

One gets the sense that Williams knows her fitness is lacking, even if she would not admit that she tired as the match wore on. Afterward, she said she could not put as many balls away late in the match, a sure sign of fatigue. And she seemed well aware that she would need more stamina to return to the top of the rankings.

“That’s the main focus for me, is just to make sure that I can play six, seven long points back-to-back without having any problems,” she said.

As Williams looks to the future, Lindsay Davenport continues to hint about her retirement.

The 30-year-old American never had the personality of Andre Agassi, on court or off. She plays a monotonous brand of tennis: Flat forehand, excellent backhand, strong serve, a stiff but serviceable volley. Speed and agility are not her forte, nor are between-the-legs winners. She doesn’t shriek on every swing, or dye her hair or don cat suits. Outlandish remarks are as foreign to her as funky jewelry.

Yet few women hit the ball more cleanly, and few, beyond a legend named Navratilova, have succeeded in the women’s game for so long. After her 6–4, 6–4 victory over Patty Schnyder, the no. 7 seeded Swiss with the loopy groundstrokes and lackluster record at Grand Slam events, Davenport is one of eight women standing at the U.S. Open quarterfinals for the 10th consecutive year — a feat more remarkable considering she saved two match points in the third round against Katarina Srebotnik.

Davenport has been consistent everywhere else, too. Since 1993, she has finished the year ranked inside the top 20. Three times — in 1998, 2002, and 2005 — she finished as the no. 1 player in the world. And while she has managed only three Grand Slam singles titles, there have been plenty of near misses, most recently her loss to Venus Williams in the 2005 Wimbledon final (in which she held match point), her loss to Serena Williams at the 2005 Australian Open (she won the first set), and her defeat, after an injury, in the U.S. Open semifinals in 2004.

Davenport has never had any desire to be the female Agassi (she called him one of a kind) and she said she has little sense of how big her following is in the world of tennis.

“Arlen [Kantarian of the USTA] was telling me yesterday that during Andre’s match at one of the changeovers, they posted I had won and there was a big cheer,” Davenport said. “I was like, ‘Are you serious?’ I couldn’t even believe that.”

As she has gotten older, though, she has sensed that people cheer for her more. Davenport knows she’ll need all their support and more against her next opponent, Justine Henin-Hardenne, who dispatched the 19-year-old Israeli Shahar Peer 6–1, 6–0 in 50 minutes.

Henin-Hardenne is in good form despite playing little since her loss in the Wimbledon final. She has decided to take to the net more, and even mix in serve-and-volley, a welcome change considering her all-court talents and her recent reliance on her baseline game.

“It’s gonna be the kind of game I will have to play in the next few years if I want to stay on the tour,” she said.

Maria Sharapova also reached the quarterfinals, recovering from a 4–1 deficit to defeat Na Li of China, 6–4, 6–2.