Serena Williams continued her undeterred march at the U.S. Open, with a 6-0, 6-0 thrashing of Andrea Hlavackova in the fourth round in New York.

Williams has hardly been troubled all tournament and it looks like it will take something extremely special from someone to even take a set from the dominant American, with Williams believing her best is yet to come.

"I honestly don't think I started out strong in the tournament," Williams said. "I feel like today I'm getting more comfortable with the court and comfortable with the conditions.

"I'm getting back to more my game, which is good. I felt like I hit better today than I had in my other matches. You know, I like to play better during the second week. Hopefully I can do that."

Williams was unrelenting against Hlavackova, not allowing her Russian opponent a sniff, even after the match was completely under the 30-year-old's control. "There is always a comeback possible," Williams said. "So I didn't want to give her that opportunity -- or anyone that opportunity -- to try to come back, especially her in particular.

"She was getting so pumped up and she never gave up. I thought that was really incredibly positive."

Williams, however, suffered defeat in the women's doubles with her sister Venus, going down to the Russian pair of Nadia Petrova and Maria Kirilenko 6-1, 6-4.

In the singles, Williams will now face Ana Ivanovic in the quarterfinals, after the former World No. 1 eased past Tsvetana Pironkova 6-4, 6-4. The fourth-round victory gave Ivanovic a place in the quarters of a Grand Slam for the first time in four years.

"I think I hardly made any mistakes in the first set," Ivanovic said. "She's a tough opponent though and I knew she was going to come back and fight hard, so the second set was tough to come through.

"It's great to be through to the quarterfinals," she added. "It's been a lot of ups-and-downs and having to take time off with injuries since 2008, but finally I've been healthy and it's showing in my tennis."

In other matches, there were a couple of upsets on view with Roberta Vinci ousting No. 2 seed Agnieszka Radwanska 6-1, 6-4. Earlier, Vinci's doubles partner Sara Errani accounted for sixth seed Angelique Kerber 7-6, 6-3.

"It was very difficult match mentally and also physically," Errani said after the match. "So it was very difficult.

"Trying to wait the other, try to do the better thing for me, the worst for her. So it was strange game also sometimes."

"It's not easy to play against someone like this that mixes the game," Kerber added. "I knew this before the match.

"I know that she will play a lot of spin and also some drop shots, but yeah, I tried to be aggressive. She was better today."