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 today and advanced 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 will meet in the semifinals.

Meanwhile, Marat Safin, last year’s runner-up, withdrew with a wrist injury from a fall in his first-round match.

The 2000 U.S. Open champion’s withdrawal sent No. 31 Rainer Schuettler into the fourth round against No. 23 James Blake, a 6-3, 4-6, 6-2, 6-2 winner over Spain’s Alberto Martin.

Safin, who had been coming back from a shoulder injury, said an injection helped him through his second-round victory over Spain’s Albert Montanes but afterward his left wrist swelled up badly.

Safin, a right-hander who hits a two-handed backhand, said it was diagnosed as a cut ligament.