MELBOURNE, Australia -- One embarrassing swing-and-miss aside, Serena Williams is steadily sharpening her game as she draws within four victories of a "Serena Slam.''

Williams needed only 46 minutes to beat Thailand's Tamarine Tanasugarn 6-1, 6-1 Saturday and advance to the fourth round of the Australian Open.

She hit 27 winners, but her eight errors included a complete miss on an overhead smash in the second set's first game.

Kim Clijsters, considered one of the most likely to stop Williams from winning a fourth consecutive Grand Slam tournament, won 6-2, 6-1 in 55 minutes against Tatiana Poutchek. She has lost just six games in six sets.

If she and Serena keep advancing, they would meet in the semifinals.

Williams won the French and U.S. Opens and Wimbledon last year.

"I've picked up my game. If I'd been at a lower level it would have been a lot closer,'' said Williams, who came close to losing her first-round match against France's Emilie Loit.

The key is staying relaxed, she said.

"I'm a perfectionist and everything has to be perfect, so if it's not going like that on the practice court, then when I get out there for the match I tense up,'' she added.

On the missed overhead, Williams said, "I didn't look at the ball, my head was down, my racket was up. It's kind of hard to hit the ball like that.''

She was expecting a hard year "because a lot of people are after me, namely Venus, who wants to be No. 1 again.''

Because of their rankings, older sister Venus is seeded in the other half of the draw and could meet Serena in their fourth consecutive Grand Slam final.

Clijsters, who beat both Williams sisters in a tournament last November, improved her record to 22 victories in 23 matches.

She has spent just 2½ hours on the court in three rounds here, but also showed a perfectionist side, throwing down her racket after a miss when the 108th-ranked Poutchek, from Belarus, held serve in the second set's sixth game.

"I think I tried to do a little bit too much,'' Clijsters said.

At last year's French Open, the 19-year-old Belgian was extended to 8-6 in the final set before beating Poutchek.

"I was really ready for revenge,'' she said.

Clijsters had a similar start here last year, losing only 15 games in five matches before losing to eventual champion Jennifer Capriati in the semifinals. Capriati lost in the first round this year.

Clijsters next meets No. 19 Amanda Coetzer, a 6-0, 6-2 winner over No. 14 Anna Pistolesi.

No. 10 Chanda Rubin reached the fourth round for a fourth consecutive Grand Slam with a 6-3, 6-2 victory over Austrian qualifier Barbara Schwartz.

She next meets No. 8 Anastasia Myskina, who reached her first fourth round at a major by beating No. 28 Clarisa Fernandez of Argentina 6-3, 3-6, 6-3.

Another Russian, Elena Bovina, beat No. 11 Magdalena Maleeva 7-5, 4-6, 7-5. She next plays No. 25 Meghann Shaughnessy.

Shaughnessy won 6-1, 6-3 against Czech player Klara Koukalova, who narrowly beat out No. 6 Monica Seles in the second round after Seles sprained her ankle in the third game.