NEW YORK -- It's funny what questions some people will and won't answer.
Take the world's top-ranked tennis player, Caroline Wozniacki.
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Her boyfriend? Sure, she's been seeing Rory McIlory of late.
Her new coach? Well, that, Wozniacki insists, must remain a mystery.
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 McIlroy, golf's reigning U.S. 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."
Does the No. 1 ranking, when it's not accompanied by a major title, feel like a burden or an honor? "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 U.S. Open, when she lost to Kim Clijsters.
She had what some viewed as a rough summer, losing her first match at both Toronto and Cincinnati -- considered key leadups to the year's last Grand Slam. But last week, she won for the fourth straight year at New Haven, and suddenly, the critics seem more like alarmists.
"I know that I'm back on track," she said. "I know that everyone has to write their stories, but I think we should move on. Ask me about something else, something more interesting."
There wasn't much interesting about this match, except maybe for the observation that Wozniacki didn't need to bring out any new weapons to defeat Llagostera Vives, the diminutive counterpuncher ranked 125th and playing her first singles match on the U.S. Open show court.
This was typical Wozniacki -- steady groundstrokes and long points, made longer on a surface that players say has been playing slower this year.
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 U.S. 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."
Elsewhere on the second day at the U.S. Open, No. 4 seed Victoria Azarenka defeated Johanna Larsson of Sweden 6-1, 6-3. She reached her first Grand Slam semi earlier this year at Wimbledon and is another good candidate to win in a wide-open women's field.
"I always take it match by match," she said. "But I have been closer to my goals, so I can only look and stay positive and keep getting better."
Serena Williams, seeded 28th but always considered a main threat, had a night match scheduled for Tuesday, as did defending men's champion Rafael Nadal. Top-seeded Novak Djokovic started his first-round match shortly after Wozniacki got off the court.
In earlier men's action, Ernests Gulbis of Latvia upset 16th-seeded Mikhail Youzhny of Russia, who made a surprise trip to the semifinals last year before falling to Nadal.
Other winners included No. 5 David Ferrer, No. 11 Jo-Wilfried Tsonga, No. 17 Jurgen Melzer and American wildcard Donald Young. No. 20 Yanina Wickmayer, No. 31 Kaia Kanepi and No. 11 Jelena Jankovic won on the women's side.