NEW YORK -- Venus Williams is playing so well that even when her serve is off she still wins.

Williams only got in 39 percent of her first serves against Sandrine Testud on Monday night, yet she was able to win 6-4, 6-0 to advance to the quarterfinals of the U.S. Open.

"Yeah, that was dismal," Williams said. "At least these days I'm serving at least 55 percent. On a good day it's like 65.

"So if I served like 70, it would be a nightmare for my opponent," she said smiling. "But it hasn't happened yet."

Williams is known for doing better in the second week of a tournament, stepping up her game as the competition gets harder.

"Like at Wimbledon, I was playing quite bad in the beginning rounds," she said. "But as soon as I got to the semifinals, I was able to play a lot better. I'm hoping this will be the same thing."

Testud certainly noticed when Williams pushed her game to a new level as the defending Open champion came back from being down 2-4 to win the last 10 games of the match.

"It's tough because she can hit the ball, you know, winners from everywhere," Testud said. "I served quite well tonight and she just returned so well."

After winning Wimbledon, Williams' confidence has grown. She says she no longer needs her father and coach, Richard, at a tournament to win.

"You know, I used to think that a little bit this year until this Wimbledon," she said. "I just wanted no one to tell me anything because I knew exactly what I wanted to do. At that point, I knew I could win on my own."

Her father did not attend the Australian Open this year, and she lost in the semifinals to Martina Hingis 6-1, 6-1.

"But you know, the reason I didn't win there was because I wasn't ready," Williams said. "So I just shouldn't have made the trip."

Richard Williams is in New York for the U.S. Open, and Williams says that although she wanted her dad to be at every tournament in the past, it's now in her hands.

"After that Grand Slam, I did know that I'm OK on my own."

Cynthia J. Faulkner is the tennis editor for ESPN.com. She can be reached at cynthia.j.faulkner@espn.com.