PARIS — Fresh off a victory over the world's No. 1 player, Nicole Vaidisova wants to savor her first berth in the French Open quarterfinals and resist any temptation to think about winning the tournament.

"That's a lot of steps ahead," said the 17-year-old German-born, Florida-based Czech. "Every match is going to be crazy tough from now on. I would love to win, but there are a lot of very, very good players out there."

That includes Venus Williams, Vaidisova's opponent Tuesday. Both rallied to win in the fourth round Sunday.

Vaidisova played the instigator in Frenchwoman Amelie Mauresmo's latest home-court meltdown, beating the reigning Australian Open champion 6-7 (5), 6-1, 6-2. Williams, the lone remaining American, swept the final four games to beat No. 7-seeded Patty Schnyder 4-6, 6-3, 6-2.

Had Williams lost, there would have been no Americans in the quarterfinals at Roland Garros for the first time in the 38-year Open era.

"Lone flag waving gently in the wind," she said.

Williams has three titles at Wimbledon and none at Roland Garros, but she's optimistic about her chances on the slower surface in Paris.

"Obviously, I like to play aggressively. It's very effective on the clay," she said. "I can still run a lot of balls down, take some pace off if I have to."

She could face a formidable challenge from Vaidisova, whose blonde hair, persistent grunts and big strokes are more than a little reminiscent of Maria Sharapova. Both are products of the Bollettieri Academy in Florida.

"It doesn't really bother me if people are comparing me to somebody," Vaidisova said. "Maria was compared to Anna (Kournikova), so everybody gets compared to somebody."

The comparison wouldn't have been so much of a compliment Sunday, when Sharapova squandered a 5-1 lead in the final set, lost 18 of the final 21 points and lost to Dinara Safina, 7-5, 2-6, 7-5.

Sharapova said rustiness following a recent injury layoff contributed to her unraveling.

"You go into a different world, and you make dumb decisions," she said.

Vaidisova and Safina are first-time Grand Slam quarterfinalists, as is Anna-Lena Groenefeld, who beat Gisela Dulko 6-3, 6-4.

Safina's opponent Tuesday will be former U.S. Open champion Svetlana Kuznetsova. Groenefeld will play two-time French Open champion Justine Henin-Hardenne, who beat 2004 champion Anastasia Myskina 6-1, 6-4.

Two-time runner-up Kim Clijsters awaits the winner of the suspended match between Martina Hingis and Shahar Peer.

Reaching the quarterfinals on the men's side were top-ranked Roger Federer, David Nalbandian, Mario Ancic and Nikolay Davydenko. The last American in the men's draw, James Blake, lost a third-round match to Frenchman Gael Monfils 6-2, 6-7 (2), 7-6 (1), 5-7, 6-4.

That left Williams to represent U.S. hopes. She likes the progress she has made in recent weeks after missing 3Z\x months with injuries.

"It's really about stepping it up at the right time," Williams said. "No matter what level I may be playing at, to know that I can take it to the next level, it's really a secure feeling."

She has faced Vaidisova only once, beating her at Istanbul last year on clay.

"I'm sure she's improved her game since," Williams said. "We have a very similar game. You know, when you match us up together, I probably can inch her out on doing things a little better."

Vaidisova will be difficult to defeat if she maintains the kind of composure she showed on center court against Mauresmo. Her calm demeanor cracked only after she smacked the last of her 38 winners on match point.