Second seed Serena Williams is bracing herself for a testing quarter-final against in-form Russian Svetlana Kuznetsova.

The American needed just 53 minutes to record a 6-1 6-2 win over her Canadian opponent on Philippe Chatrier court.

Kuznetsova, the seventh seed, found things more tricky in her triumph over Poland's Agnieszka Radwanska but the set she lost in the 6-4 1-6 6-1 victory the first the Russian had dropped this tournament.

Kuznetsova is also the only woman to defeat world number one Dinara Safina on clay this year.

Williams said: "She's an excellent clay-court player. She's been playing unbelievably well.

"This is when everything counts. I have to pick up my level and play a strong match, especially when playing somebody like Svetlana, who moves extremely well and doesn't do anything bad."

Click here to view pictures of Day 9 in the French Open.

Williams, the 2002 champion, had a real battle against Maria Jose Martinez Sanchez in the third round, coming through in three tight sets.

But she found it much easier today, breaking in games two and six to take the first set comfortably.

Wozniak, the 24th seed, did manage a break herself, in the sixth game of the second set. But that was as good as it got for the Canadian.

"I feel like it was my most focused match so far," Williams said.

Kuznetsova survived a mid-match wobble to defeat Radwanska, the 12th seed, on Suzanne Lenglen court.

"I was really nervous today - I don't know why," said Kuznetsova.

"It was tough mentally. In the next match, I cannot allow myself to do this. I'll have to be more prepared."

Kuznetsova lost to Williams in the quarter-finals of the Australian Open earlier this year, and the American has won 10 majors in total down the years.

"Maybe she hasn't played that many tournaments on clay, but you cannot discount her," said Kuznetsova.

"She's a big champion, she's won here and definitely knows how to play on clay."