Anna Kournikova fought her way out of trouble and into the final 16 at the Australian Open on Friday, as her private life was once again splashed across the newspapers.

The Russian 11th seed, whose glamorous appearance guarantees her more column inches than her playing record merits, beat Czech Kveta Hrdlickova 2-6 6-3 6-4.

After an awful first set the 18-year-old soon picked up her game and had few problems battling back.

Kournikova said she was looking forward to a re-match in the next round with second seed Lindsay Davenport, who beat her last week in the semifinals of the Sydney international.

"I like to play against (Davenport). We've had some good matches in the past," said Kournikova.

"But definitely it's going to be a tough match."

Kournikova refused to discuss a report in the Herald Sun newspaper linking her romantically with Melbourne's own Mark Philippoussis.

The pair were reportedly seen kissing in a car park this week, but both said there was no romance.

"I know him from Florida. I've known him for a very long time. We played juniors together," she said.

"I'm not saying anything. I would not want to discuss my private life. No comment."

When asked about the report after Kournikova watched his third round victory, Philippoussis said: "I just laugh at it."

Davenport awaits Kournikova after an effortless 6-0 6-1 victory over another Russian, qualifier Alina Jidkova.

The Wimbledon champion anticipates a tougher battle against her better-known Russian opponent.

"I know she wants to do well, especially in a Grand Slam. I know she'll be fired up," said Davenport.

Fourth seed Mary Pierce won her third round clash over Miriam Oremans of the Netherlands 6-2, 6-4.

Pierce must now play a woman who has won their last two meetings.

Japan's Ai Sugiyama, ranked 24th in the world, recovered from a break down in the first set to beat Sweden's Asa Carlsson 6-4 4-6 6-3.

The Japanese no 1 expects a tougher ride from Pierce next week following her successes in San Diego and Moscow last year, and a doubles win over the French woman last week.

"It's a different feeling playing a top 10 player or a seeded player at a Grand Slam," said Sugiyama.

"I have nothing to lose - I'll go for it and just see how things go."

Elsewhere French ninth seed Julie Halard-Decugis, beat Russia's Elena Dementieva 3-6 6-4 6-2.

Jennifer Capriati overcame China's Yi Jing-qian in straight sets.