Anna Kournikova is known for the swish of her long blond hair, for the curve of her often-exposed back, for the length of her dangling legs. She is not known for her tennis.

In a way, this is fair, considering that Kournikova has never won a tournament on the WTA Tour, not even a minor, lower-tier event. But in a way, it is not, because Kournikova definitely can play tennis, and between all those swishes and winks and nods there are some excellent volleys and an impressive mix of ground strokes.

In all, she has shown much at the Australian Open, winning her first two matches with succinct authority and overcoming an early deficit against gritty Czech Kveta Hrdlickova in the third round this morning to claim a 2-6, 6-3, 6-4 victory.

But the circus that surrounds the 18-year-old Russian is never too far away, and the noise can be distracting. Kournikova's fourth-round match likely will be even tougher. She will face No. 2 seed Lindsay Davenport if Davenport can win her match against qualifier Alina Jidkova tonight--and many will be watching to see if Kournikova finally can establish a place among the WTA Tour's top players.

"She's going to have to show herself where she is," said Martina Hingis, who played doubles with Kournikova last year. "She's got a new coach, and she has to prove herself."

Hingis, who won her own singles match, 6-3, 6-3 over Justine Henin Thursday night, is here with a new doubles partner this year, as is Kournikova. Neither has explained their split publicly--they remain friends off the court--but the perception is that Hingis grew frustrated with Kournikova's weak service game and less-than-maniacal work ethic.

Kournikova has tried to improve in these areas, especially her serve, which spit double faults at this tournament last year. So far this year her serve has been excellent, and in her first two matches she did not drop a service game. She won her first 17 games as she defeated Patricia Wartusch, 6-0, 6-0, and Natasha Zvereva, 6-1, 6-4.

Kournikova's famous body has also been under reconstruction, with new coach Eric Van Harpen putting her through more rigorous workouts and tougher weight training.

"We're focusing on my fitness and just mainly bringing my game together to be more consistent," she said. "To be patient on the court and to be a more consistent player, you need to be in good shape, so that's what I'm working on."

But while Van Harpen has been giving Kournikova some more stability on the court, her life off of it has remained tumultuous. Her romantic interests, always under scrutiny, have been even more closely examined of late, especially since she became friendly with Pavel Bure, the talented Florida Panthers winger.

Bure has sold his apartment in Fort Lauderdale to move to the Miami building where Kournikova lives. Kournikova, who long had been linked with Red Wings star Sergei Fedorov, has shown up at several Panthers games.

The Florida press has run with the story, with one newspaper reporting that, according to Dade County records, the $3 million apartment Kournikova lives in--and that Bure is presumably spending time in--originally was bought by Fedorov, who then sold it to Kournikova for $100.

Kournikova declined to discuss her love life with the media here, although she did say that the kisses she blows at the end of each match are for "someone special" who is "on the other side of the ocean."

That hasn't stopped her from making a few friends on this continent as well. Kournikova has sat in Australian Mark Philippoussis's box for his last two matches, and while she said today that she and Philippoussis are "friends," she was coy enough to ensure several more days of frenzy in the local media. Kournikova clearly likes the attention, although she also intends to provide just as big a show on the tennis court as she has in her news conferences.

"There's a time for everybody," Kournikova said. "It's going to come, going to work. I have very good results. I'm number 12 in the world, and it's not for nothing."