updated 11:54 p.m. ET Aug. 30, 2008

NEW YORK - Less than two months ago, the Williams sisters played each other in the Wimbledon final.

Because of the quirks of rankings and the vagaries of tournament draws, they are on track to meet in the U.S. Open quarterfinals.

Is that disappointing?

“Obviously, yeah,” Serena Williams said. “But I’ve had over a week to think about it. So right now I’m just hoping to win my next match.”

Neither Williams had the least bit trouble advancing to the fourth round at Flushing Meadows. Both won 6-2, 6-1 Saturday against seeded opponents.

The No. 7-seeded Venus Williams beat No. 27 Alona Bondarenko of Ukraine, and not long after, in the same Arthur Ashe Stadium, No. 4 Serena Williams defeated No. 30 Ai Sugiyama.

“I would have loved it if we could have met in the final,” Venus told the crowd. “My biggest worry is that she’s so good. Sorry, but I’m thinking about how I’m going to get past her.”

One statistic was particularly compelling: Venus compiled a 32-4 edge in winners against Bondarenko.

“She’s playing really well, and I’m glad she feels like she’s playing her best. It’s nice to feel like when you’re playing your best,” Serena said. “Right now I’m not playing my best, but that means I can do so much better.”

First things first, though.

Venus will face No. 9 Agnieszka Radwanska of Poland, who eliminated No. 18 Dominika Cibulkova of Slovakia 6-0, 6-3. Serena will meet Severine Bremond of France, a 7-5, 3-6, 6-4 winner against Tathiana Garbin of Italy in a match that ended shortly before midnight.

Julie Coin’s magical stay at the Open is over. The world’s 188th-ranked women’s player upset Ivanovic on Thursday, but her run ended in the third round with a 6-4, 6-4 loss to fellow Frenchwoman Amelie Mauresmo, the No. 32 seed.

In Radwanska, Venus takes on someone who upset then-defending champion Maria Sharapova at the U.S. Open last year. And someone who beat Venus the only time they played.

Still, Venus said: “I have a very good feeling about the next round. I saw Serena play against her. I don’t know how to say her first name too well.”

For the record: ag-nee-ESH-ka.

There isn’t much in the way of household names left in the women’s field. Not only are the Williams sisters the only past U.S. Open champions around, consider this: Venus and Serena Williams have won a total of 15 major singles titles, while the other 14 women who will be in the round of 16 at Flushing Meadows have a combined total of two major singles titles.

From 1999 to 2002, one Williams or the other won the U.S. Open. But neither has even been to a final at the hard-court major championship since that run — Venus has only reached the semifinals once, and Serena hasn’t been past the quarterfinals.

Yet ever since both bowed out in the third round at the French Open, the sisters have been playing quite well.

They met in the final at the All England Club in July, when Venus won her fifth title there. They also teamed to win a gold medal in doubles at the Beijing Olympics.

With players such as Sharapova (injured), Justine Henin (retired), Ana Ivanovic (lost), Lindsay Davenport (lost) and Svetlana Kuznetsova (lost) out of the way at the U.S. Open, things only get easier for the Williams pair.

Except, of course, in the quarterfinals.

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