Improving Serena welcomes progress

Williams, the eighth seed, had not been sharp in her opening encounter on Monday but still moved on in straight sets past Germany's Angelique Kerber as she came back from a left-thumb strain. And the 1999 and 2002 champion was far from fluent in getting past against Italian Maria Elena Camerin, relying on her power to win 7-5 6-2 at the Arthur Ashe Stadium.

"I feel a lot better than I did in the first round, that's for sure," Williams said on court after the match. "I've still got to get it together, though."

She added: "She played a great game and all credit to her, but I'm definitely getting a lot stronger and feeling a lot better and I'm happy to be out here."

Third seed Jelena Jankovic beat Olga Govortsova of Belarus 6-2 6-2 on the Louis Armstrong Stadium court.

Jankovic reached the semi-finals of a slam event for the first time here 12 months ago but has been handed a tough draw in the same quarter as Wimbledon champion Venus Williams and her compatriot fifth seed Ana Ivanovic, both of whom won easily earlier in the day to remain on course for a fourth-round showdown.

Ivanovic kept her part of the bargain with a second-round 6-3 6-1 victory over France's Aravane Rezai in the opening match at Arthur Ashe Stadium, while the American followed her onto the show court and beat unseeded Romanian Ioana Raluca Olaru 6-4 6-2.

Like Ivanovic, top seed Justine Henin suffered a first-set break of service before turning up the pressure and blasting past her second round opponent.

The Belgian sealed her place in the third round with a 6-4 6-0 defeat of qualifier Tsvetana Pironkova of Bulgaria.

Tenth seed Marion Bartoli booked her place in the third round with a 6-4 6-2 win over Italy's Sara Errani while number 14 Elena Dementieva beat Czech qualifier Petra Cetkovska 6-3 6-2 in an hour and 12 minutes on Court 11 and Dinara Safina eased past second round opponent Ukrainian Kateryna Bondarenko, 6-2 6-1.