There is nothing extraneous floating in the head of Ana Ivanovic, the Serb who once practised her tennis in a drained swimming pool. The French Open champion has come to Wimbledon fully focused on the task of winning back-to-back Grand Slams. So the talk, in her breathless English, is purely technical, embracing ideas such as adopting a playing stance with a lower centre of gravity to help cope with fast balls on the grass of Centre Court.

By contrast, the subject matter clogging the brain of Serena Williams is so extraordinarily eccentric that it is a wonder the drawling American is able to concentrate long enough on her game to make a single serve, let alone go all the way to a third title.

Take Barack Obama, the US Presidential candidate to whom she would give her vote if she could, but she can't so she won't. Then there's the gold stitching she noticed inside the trench coat she wore onto a sun-baked Court One yesterday.

With Ivanovic, you just know the 20-year-old top seed will be as totally committed tomorrow, when she plays Nathalie Dechy of France for a place in the third round, as she was yesterday in sweeping aside Paraguay's Rossana De Los Rios 6-1, 6-2.

With sixth seed Williams, who was forced to save five break points in the opening set before seeing off hard-hitting Estonian Kaia Kanepi 7-5, 6-3, you simply don't know who will turn up.

Will it be the super aggressive righthander whose determination to overcome injuries that would have beaten weaker souls has proved such an inspiration? Or will it be the celebrity fashionista who flopped so desperately against Slovenian Katarina Srebotnick in the third round of the French Open?

Ahead of her second round test here tomorrow against wild card Urszula Radwanska of Poland, the fashionista looked like holding sway.

That coat was clearly close to her heart. "You know, I absolutely love trench coats," she revealed: "I probably have more coats than anybody. I just love coats. And I don't know why because I live in Florida (the Sunshine State) so it doesn't really add up."

The coat was made specially for Williams by Nike. She said: "Now I have a wonderful white coat I can wear on the court and also, you know, in New York for those rainy days."

Tell us more, Serena. "It's a very lightweight fabric. It's a woven so it has a little give in it as well. On the inside it's stitched with gold. It's just delectable."

Like Obama? Williams was off again, this time on the election trail. "I obviously am excited to see Obama out there doing his thing," she said. "But I'm a Jehovah's Witness so I don't get involved in politics.

"We stay neutral. We don't vote. We don't get a part of those worldly things, so I'm not going to necessarily go out and vote for him. I would - if it wasn't for my religion."

Obama still has some work to do before he becomes the main man in Washington, but Ivanovic is firmly ensconced as number one in SW19. And she is relishing the boost to her confidence that comes with that ranking.

She said: "There's the expectation of achieving one of your biggest dreams and goals. That's something that's new for me and I'm enjoying it."

Even the pressures that come with being the woman to beat? Ivanovic, who lost to Serena's sister Venus, the eventual champion, in last year's semi-finals, replied: "There are different ways of dealing with pressure. Becoming number one means more pressure, but you have to take the pressure for what it is.

"It is a reflection of your own ambition. It's something, if you see it as a positive thing, that means you're in a position to do something memorable. If you look at it that way it can be very motivating." Flashing a smile, Ivanovic appeared relaxed following her memorable triumph at Roland

Garros earlier this month, as though a weight of expectation has been lifted from her shoulders and now she can simply concentrate on her game. That could spell danger for her rivals.

"I'm still basically the same person," she said. "The only thing that I feel changed a little bit is I have a little more confidence.

"And winning a Grand Slam, it's been my dream since I was a kid. I was in two finals before so actually making one more step and winning, that's something that makes me very happy."

Winning undoubtedly makes Williams happy, too. But as happy as wearing a gold-stitched, woven trench coat in the midst of a London summer?

What a glorious addition to the Wimbledon scene she is. But she's not alone. Williams insisted: "There's so many bright faces out here, different games, different styles. I just think nothing stops, the world keeps turning."

So does Planet Serena, and thank goodness for that.