Serena Williams was on her best behavior and ominously close to her top form when she made her long-awaited appearance at the U.S. Open Tuesday.

There was no repeat of the foul-mouthed tirade that she disgraced herself with a Flushing Meadows two years ago.

This time, she was all smiles and business usual when she demolished Serbia's Bojana Jovanovski 6-1 6-1 in less than an hour.

I'm always glad to be done with that first round, Williams told reporters. I feel like when I'm done with that, then I can kind of go through and just play.

I'm glad that one's over. It took a long time, it seems.

It was a clinical and ruthless display from Williams, who has won the U.S. Open three times, but is still on probation for her outburst two years ago.

On that occasion, she unleashed a foul-mouthed tirade at a line judge and was docked a point that cost her the match against eventual champion Kim Clijsters.

I feel fine. Even last time I played here, Williams said.

I went out with a bang. I came in with a bang tonight. So it's all good.

Williams was also handed a $175,000 fine that was halved on condition that she did not misbehave for another two years. Her probation period expired next month.

During that time, Williams has won two grand slam titles and missed three because of a foot injury that led to other health complications, including a potentially fatal blood clot on her lung.

Williams made her return this year and won lead-up events in California and Toronto to wrap up the U.S. Open series. The 29-year-old has been installed as one of the favorites to win this year although she is less certain.

I'm just here to play. Everyone's been playing all year and I haven't, she said.

I've played like five tournaments this year. I don't think that's usually a favorite going into another grand slam.