NEW YORK - Venus Williams wants more.

More matches, more victories, more Grand Slam titles.

“Yeah, I definitely would love double-digits” in major championships, said Williams, who won No. 6 at Wimbledon in July and hopes to get No. 7 at the U.S. Open this weekend. “Definitely had a few years there where some Slams were lost between injuries and a lot of other stuff happening.”

Consider this: Friday’s showdown with No. 1 Justine Henin will be Williams’ first semifinal at Flushing Meadows since 2002.

Now look at things from the Belgian’s perspective: She had to deal with Serena Williams in the quarterfinals and must try to become only the second woman to beat both sisters during a single Grand Slam tournament. The only time it happened was at the 2001 Australian Open, where Martina Hingis eliminated Serena in the quarterfinals and Venus in the semifinals — only to lose to Jennifer Capriati in the final.

“It will be a good challenge for me to play both sisters in the same tournament,” 2003 Open champion Henin said, mastering the art of understatement.

Taking all tournaments into account, the Williams sisters have lost to the same player at an event a total of five times in their decade on tour. On 11 occasions, a woman made it past one Williams, then lost to the other.

After edging No. 3 Jelena Jankovic in a third-set tiebreaker Wednesday night, Venus Williams made a point of saying she watched Henin beat Serena — and that she wants to play well Friday to uphold the family’s honor.

Henin has to be aware, as well, that she is 1-7 against the older Williams, with her only victory coming in their very first match, on clay at Berlin way back in 2001.

There is, let’s not forget, another semifinal Friday, with No. 4 Svetlana Kuznetsova facing No. 6 Anna Chakvetadze in an all-Russian matchup. Kuznetsova won the 2004 U.S. Open and also reached the 2006 French Open final, while Chakvetadze never before made it beyond the quarterfinals at a major.

Neither will be given much of a chance in the final, regardless of whether the opponent is Williams or Henin.

“Venus and Justine will be a great match,” Jankovic said, “and I think one of them will win the whole tournament.”

In the men’s semifinals Saturday, No. 1 Roger Federer will play No. 4 Nikolay Davydenko, while No. 15 David Ferrer meets No. 3 Novak Djokovic or No. 17 Carlos Moya.

Three-time defending champion Federer took the day off Thursday, skipping practice and resting after beating 2003 Open winner Andy Roddick in a match that began Wednesday night and ended after midnight.

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Ferrer, who upset Rafael Nadal in the fourth round, beat No. 20 Juan Ignacio Chela 6-2, 6-3, 7-5 Thursday. Djokovic was scheduled to play Moya at night.

Late Thursday afternoon, Venus Williams put in a practice session, pausing for a moment to get her right shoulder massaged by her boyfriend, pro golfer Hank Kuehne.

It has been quite some time since she was at the height of her powers in New York, swatting big serves and groundstrokes and using all of her 6-foot-1 frame to get to everything back along the baseline and cover all angles up at the net.

She fared no worse than reaching the semifinals at the U.S. Open every year from 1997 to 2002, winning the 2000-01 titles and finishing as runner-up twice. Her game can be as intimidating as anyone’s in women’s tennis when she’s healthy — and Williams sure looks in fine form at present.

“Venus is moving extremely well,” her father and coach, Richard, said earlier in the tournament. “From what I can see, Venus is moving better than anyone who’s playing right now.”

Williams arrived in New York late last month and essentially said she was merely happy to be here. She missed the 2006 U.S. Open because of an injured right wrist, part of a lengthy layoff that put her at No. 46 in the rankings at year’s end.

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She was at No. 31 entering Wimbledon, and became that major’s lowest-ranked women’s champion ever.

She was at No. 14 entering the U.S. Open, and her run so far already assures Williams of getting back into the top 10 next week for the first time since April 2006.

A victory over Henin would push Williams to No. 7.

In her mind, of course, she’s No. 1.

“I always think that I’ll be on top. I never think that I’m not the one,” Williams said. “I believe always I’m the one — and when I’m not the one, it really bothers me.”