Williams has always had extraordinary physical flexibility - there are times when she stretches so far to retrieve a wide ball she performs the splits - but lately she is beginning to loosen up in other ways too.
"It's important to stay composed," she said after her 17th grand slam title at the US Open. "I've been doing that a lot since I came back [from the foot injury and embolism that kept her out for much of 2010 and 2011] I am an emotional person, an emotional player, but I definitely think I am better at being calm and more relaxed."
Friday's match offered a good example because Williams was not quite at her best. Groundstrokes kept ballooning long, as her feet failed to move on another 40-degree morning. But her thought processes, at least, remained cool. She knew Hantuchova did not have the weapons to topple her. As usual, the only player who could have beaten Williams was herself. After a few anxious moments at the end, she guided a forehand up the line to seal the win on her fourth match point.
This was her 61st victory at the Australian Open, carrying her past Margaret Court to the top of the all-time table. Is she still getting better?
"I don't know," she replied. "I feel like 32 is young in life. In sports, it's old. But for whatever reason, I feel like I just never was really able to reach my full potential and I feel like recently I have been able to do a little better. I just keep trying to improve."
In the fourth round, Williams can look forward to a favourable draw against Ana Ivanovic, who has not taken a set off her in four meetings.
There are probably only two women with a chance of stopping her left in the draw, and one of them, Li Na, was a point away from going out of the tournament on Friday.
"The five centimetres saved my tournament," said Li, who could only watch as Lucie Safarova went for a booming backhand winner on match point. Although the ball travelled so perfectly down the sideline it could have been calibrated by a laser, it flew fractionally long, and Li came back to win 1-6 7-6 6-3.
On the men's side, Novak Djokovic continued his relentless march, stacking up his 27th straight win since last year's US Open and his 24th in a row at the Australian Open, where he has not been beaten since 2010. His victim this time was Denis Istomin, beaten 6-3 6-3 7-5.
It was a bad day for the French, who had a remarkable eight men in the last 32 but all three who played Friday - Jeremy Chardy, Edouard Roger-Vasselin and Richard Gasquet - go out of the tournament. Gasquet was the second top-10 seed to fall, as he lost 6-2 5-7 4-6 6-7, against Tommy Robredo.
