Venus Williams won the US Open in 2000 and 2001

Venus and Serena Williams each stormed through their US Open third-round ties to stay on course for a quarter-final showdown at Flushing Meadows.

Wimbledon champion Venus was on court for less than an hour as she thrashed Ukraine's Alona Bondarenko 6-2 6-1.

And Serena was equally untroubled in beating Japan's Ai Sugiyama 6-2 6-1.

Sixth seed Dinara Safina had a much tougher test, recovering from a set down to beat unheralded Swiss teen Timea Bacsinszky 3-6 7-5 6-2.

Safina committed 41 unforced errors as she scraped past 19-year-old Bacsinszky, who was playing in the third round of a Grand Slam for the first time.

The Russian, one of a clutch of players who could emerge from the tournament as world number one, now meets Germany's Anna-Lena Groenefeld.

Groenefeld became the first female qualifier since Anna Kournikova in 1996 to reach the US Open fourth round by defeating France's Alize Cornet 6-4 7-5.

Serena plays France's Severine Bremond after she beat Tathiana Garbin of Italy 7-5 3-6 6-4, while Venus faces Agnieska Radwanska for a chance to reach the last eight.

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Ninth seed Radwanska, 19, cruised past Slovakia's Dominika Cibulkova 6-0 6-3 in 76 minutes and stands in the way of another Grand Slam meeting between the Williams sisters.

"I would have loved if we could have met in the final," said Venus. "My biggest worry is that she is so good. I'm worried how I'm going to get past her more than anything."

As for her last 16 match-up against Radwanska, Venus admits she will have to be wary of an opponent who won their only other encounter, in Luxembourg two years ago.

"I'm looking forward to evening the score," said Venus.

"She played well that time. But I'm looking forward to continuing to serve well, move well and play well out here."

Amelie Mauresmo reached the fourth round of a Grand Slam for the first time this year, ending Julie Coin's shock run in the process.

Qualifier Coin defeated top seed Ana Ivanovic in the previous round but fellow Frenchwoman Mauresmo proved too strong, winning 6-4 6-4.

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