No 1 seed Williams saw off qualifier Emilie Loit 6-4, 6-1, but was made to work much harder than she had done in her opening two matches.

The 10-time Grand Slam-winner, playing in her first event since winning the Australian Open, had her serve broken for the first time in the tournament in a close first set, before running away with the match in the second.

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"I'm very happy with my game. It's cool. I'm always trying to win the big tournaments and this is one of my favourites," said Williams.

Second seed Jankovic, meanwhile, fought back from a set down to overcome fifth seed Alize Cornet 5-7, 6-4, 6-4 in a keenly contested match that lasted over two and a half hours.

In front of passionate home support, 19-year-old French No 1 Cornet survived an early break of serve to take the first set, but was unable to keep pace with Jankovic as the Serbian upped the tempo to secure her passage to the last four.

"It's never easy to play a local player," Jankovic said. "Her fans were really backing her up. But this crowd has quite a sense of fair play. They were applauding my points along with hers."

Cornet, meanwhile, was left to rue another near-miss against Jankovic, having previously taken the former World No 1 to three sets at the 2007 US Open.

"I'm not far away," she said. "I manage to worry (the top players) but there's always a little something missing. Maybe I just need one big victory to get there."

Wild card Nathalie Dechy had booked her place in the last eight with a three-set victory over sixth seed Patty Schnyder of Switzerland late on Thursday, and the effort of her exertions showed as she was overpowered by Olympic champion Dementieva 6-3, 6-2 in just over an hour.

"I've had a fever and I was a bit short on juice," Dechy reflected. "Against a player like Elena, who has an exceptional return, it just doesn't work."

It was left to Mauresmo to save face for the French supporters, and she took a little under 70 minutes to dispose of World No 10 Radwanska, saving six break points over the course of the match and serving and returning with imperious authority.

"I was really solid, 6-2, 6-0, it's fantastic. I was expecting more of a fight, but I felt her collapsing as the match went on," said Mauresmo, a winner here in 2001 and 2006.

Dementieva's victory means she will meet Williams in the semi-finals later today, while Jankovic must face the in-form Mauresmo.