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Caroline Wozniacki Image Credit: AFP

New York: Caroline Wozniacki opened her latest quest for her first Grand Slam title with a 6-3, 6-1 victory over Nuria Llagostera Vives of Spain on Tuesday.

It was a drama-free match in Arthur Ashe Stadium that left the most interesting stuff for the post-match interview.

How were things going with Rory McIlroy, golf's reigning US Open champion whom she started dating this summer?

"You know, he has something I'm looking for and I have something he's looking for," she said. "He wants to be No 1. So it's good to have something on each other."

Mystery coach

Does the No 1 ranking, when it's not accompanied by a major title, feel like a burden or an honour? "I'm trying to stay up there as long as possible, and it doesn't really matter what people are saying," she said. "No one can ever take that away from me."

And why not end the suspense and tell us who that new coach of yours is?

"Yeah, well, I have to respect him, as well," she said. "So if he wants to be in the background and not have his name out, I have to respect that."

Though she's refusing to name names, Wozniacki is clearly looking for another gear and a few more weapons as she tries to add to a resume that includes 46 of the last 47 weeks at No 1 but no major championships and only one trip to a Grand Slam final — two years ago at the US Open, when she lost to Kim Clijsters.

A number of the ex-players, who now work as analysts on TV, say Wozniacki's kind of game isn't suited to winning Grand Slams, especially not the kind of grind that the US Open can be.

Wozniacki isn't listening.

"They can say what they want," she said. "I'm the type of player I am. I've won a lot of tournaments. I'm No 1 in the world, and of course I can still improve. There are a lot of things to my game I can still improve, but everyone can."