NEW YORK -- Confidence has always been an issue for Serena Williams and Lindsay Davenport.

	Lindsay Davenport wipes her face during her match against Serena Williams on Tuesday night.

Williams, it seems, sometimes has too much, while Davenport can never seem to have enough.

On Tuesday, their respective self-esteems collided in a titanic quarterfinal match at the National Tennis Center. In the end -- and only at the very, very end -- did Williams win the battle 6-3, 6-7 (7), 7-5.

Williams blew two match points in a second-set tiebreaker and threw away a 4-2 lead in the third set after leading 40-love, but she prevailed in two hours and 14 electrifying minutes.

Now Williams faces top-seeded Martina Hingis in a semifinal match on Friday. A victory there could set up another historic but logical first for the Williams sisters: Venus and Serena could meet for the first time in a Grand Slam final.

"Obviously, I'm tired of losing close matches," Williams said. "I really, really wanted to win this match.

"I always have a lot of self-belief. Everyone points out the close matches that I lost, but you've got to let that go, you really do, or else you're just going to be in a hole forever."

Said Davenport, "She's a great competitor. Came back after being match point up. Blew a lead again. Hung in there. That's tough to do sometimes.

"I mean, it seems like she has a slight pattern of doing that, sometimes letting the person back in the match. I guess she's getting better at dealing with it."

The difference in the match? It was Williams' ability to scramble to net and finish points. She converted an astounding 24 of 27 opportunities, 89 percent, compared to Davenport's 13-for-19 (68 percent).

When Williams won the 1999 U.S. Open at the age of 17 she beat Venus, 15 months her senior, to the family's first Grand Slam singles title. It became fashionable to say that Serena, not Venus, would have more success within the family. And then Venus won three of the next seven Grand Slams, while Serena struggled with injuries and the trappings of stardom. Sometimes in matches, her concentration wandered away and never came back. Unforced errors, a reasonable measure of concentration, tended to run ahead of winners.

Venus, goes the prevailing opinion, is mentally tougher than Serena.

This year, Serena's inactivity has cost her in the seeding process. Instead of seeing the best players in the semifinals and finals, she began facing the Hingises and Capriatis in the quarterfinals. In fact, in all three major tournaments this year, Williams was eliminated by either Hingis or Capriati in the quarters -- and all three matches went a taut three sets.

"Comes a day when someone gets tired of losing in the quarterfinals all the time," Williams said. "I would like to move ahead, just go three steps farther than the quarterfinals."

Last week, Williams admitted she wasn't taking the game seriously enough and vowed to bear down and play more matches next year. Well, it looks like she's starting early.

Williams beat Capriati in the final at Toronto two weeks ago. Williams lost her first set here at the U.S. Open and then won the next six sets, losing only six games in the process.

Davenport, of course, is no Anca Barna or Denisa Chladkova or Martina Sucha. Until this year, Davenport had won a Grand Slam singles title in each of the three previous years.

From the beginning, the match was Williams' to lose. Loose and smooth, Williams would run out to a lead, only to tighten up and see it disappear. She broke Davenport in the eighth game of the first set and successfully coasted, pretty much for the last time.

Up a break at 3-1 in the second set, Williams lapsed and found herself in a second-set tiebreaker. At 6-5, she pounded a loose backhand long and missed a chance to close out the match. At 7-6, she lost another match point when Davenport crushed a backhand just inside the baseline. Davenport leveled the match when Williams' backhand sailed long.

The third set offered more hysterics. Williams actually led 4-2 and had a 40-love lead when she double-faulted -- perhaps the perfect microcosm of a confidence crisis in tennis. Davenport fought her way back to deuce and finished the break with a strong cross-court forehand. Davenport served to draw even at 4-all and the match continued on serve until Davenport stepped up to serve herself into the third-set tiebreaker.

Williams hit a backhand winner of a second serve to gain her third match point. On this ultimate point, Williams was never more focused. She stretched for Davenport's big first serve, then ran down two more deep shots on the forehand side. The winner was a forehand cross-court shot that left Davenport flat-footed.

In the critical yin-yang area of winners vs. unforced errors, Williams' winners carried the day, 44-40.

After congratulating Davenport at net, Williams leaned back and screamed, "Yesssss!" and pumped both of her fists.

Where did that champion's mindset come from? As it turns out, from older sister Venus. "Venus told me something really important the other day," Williams said. "She said, 'You know, champions in tight situations are able to pull through, they don't get nervous.' That really helped me a lot.

"I don't have time to be nervous anymore. I'm like, `You know what, doesn't matter. I just shouldn't get nervous. I should just go ahead and do the best I can.' "