updated 6:52 p.m. ET Sept. 1, 2008

NEW YORK - By now, Venus and Serena Williams know all too well how it feels to set aside sisterhood for a couple of hours and try to beat each other on a tennis court.

They know what it feels like to meet at a Grand Slam tournament, what it feels like to win such a match, what it feels like to lose.

And they much prefer it when there’s a major championship at stake. The all-Williams showdown, set up by their easy victories Monday at the U.S. Open, comes earlier this time.

This time, Williams vs. Williams is only a quarterfinal.

“It’s so soon,” Serena said. “You know, it’s just disappointing to be so soon.”

Both advanced through the fourth round without a challenge. The No. 7-seeded Venus dismissed No. 9 Agnieszka Radwanska of Poland 6-1, 6-3, before No. 4 Serena dispatched wild-card entrant Severine Bremond of France 6-2, 6-2 at night.

“Even the semis would have been better than the quarterfinals, but at least one of us will make it to the semis,” Serena told the crowd during an on-court interview. “I’ve got probably the toughest match of the tournament coming up next, so I’ve got to be ready.”

Some sisters make plans to go shopping together, say, or to catch a movie. These siblings keep running into each other at their sport’s highest levels.

Venus beat Serena for the title at Wimbledon in July — their seventh major title match — and Wednesday will mark the first time they’ve squared off at consecutive Grand Slam tournaments since 2003.

Both have dealt with injuries and inactivity that stalled their dominance, but clearly they are back at the height of their powers.

“The best part is that we’re still here,” Venus said, “going stronger than ever, in my opinion.”

They’ve played 16 times as professionals, with each winning eight. That includes 10 meetings at major tournaments, with each winning five.

“I would love to have a winning record,” Venus said. “I have a chance.”

Because of the luck of the pre-tournament draw, they were placed in the same portion of the bracket in New York — much to the disappointment of them, U.S. Open organizers and TV types. Even other players.

“For sure, it would have been better for the crowd if it was a final,” Bremond said. “It would have been a very good final.”

That certainly rings true: Serena has lost a total of 14 games through four matches at Flushing Meadows; Venus has dropped 15.

Of the eight women left in the tournament, only two have won a Grand Slam title — Serena leads all active players with eight, and Venus is right behind with seven.

They won every U.S. Open women’s singles championship from 1999 to 2002, meeting in the finals the last two years of that span — it was their ascension that prompted the U.S. Open to move the women’s final from Saturday afternoon to Saturday night. Since 2002, though, Serena hasn’t made it past the quarterfinals here, and Venus has only reached one semifinal.

“I just feel like, you know, we’re both playing better and feeling better,” Serena said. “We just had a turn in our careers. We’re just playing the way we should play.”

Also advancing Monday were No. 6 Dinara Safina, who defeated Anna-Lena Groenefeld 7-5, 6-0, and No. 16 Flavia Pennetta, who beat No. 32 Amelie Mauresmo 6-3, 6-0.

Venus faced what theoretically should have been an opponent to be taken seriously: Not only is Radwanska ranked in the top 10, but she won her only previous match against the elder Williams sister and she upset then-defending champion Maria Sharapova at last year’s U.S. Open.

Radwanska needed 27 minutes just to claim a game this time, and never came up with a reply for Venus’ constant forays forward. Venus won the point 25 of 34 times at the net, and she put together a remarkable 33-11 advantage in winners.

“She was playing very aggressively, going to the net all the time. There was nothing I could do,” Radwanska said. “She was too good.”

Bremond offered essentially the same analysis after trying to slow Serena, who finished with a 24-10 edge in winners.

Asked to define her on-court sibling rivalry, Serena called it “classic” and “unique.”

No argument there.

What about “difficult,” given the prospect of trying to have success at a sister’s expense?

“No. Not anymore,” Serena replied. “Just another match. Another possibility for me.”

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