EASTBOURNE, England—Today, I’m spending time with one of my favorite players, Petra Kvitova—also known, to the spectators who wander past her match with Monica Niculescu on Court 2, as, “Is that the girl who won Wimbledon?” Or, alternatively and more damningly, “She isn’t the girl who won Wimbledon, is she?” The latter was overheard as the Czech frames a forehand out of Devonshire Park.

The answer to that question is, of course, yes—and then again, no. When Kvitova opens the match by racing to a 4-0 lead, peeling off winner after winner in glorious succession, she looks exactly like the 21-year-old who marched straight to the Wimbledon title two years ago, the player who neither Victoria Azarenka nor Maria Sharapova could slow down for more than a moment, whose big lefty forehand and distinctive celebratory yelp instantly became famous.

On the other hand, when Kvitova is broken in a welter of unforced errors and has to toil mightily to get the ball inside the lines before finally closing out the first set, 6-4, she looks like the woman who’s struggled to match that success ever since, suffering some surprising, even inexplicable, defeats. Part of that, of course, has to do with Niculescu, whose game is predicated upon getting a lot of balls back and making life as difficult for her opponents as possible.

In that sense, it’s a good win for Kvitova, better than Niculescu’s ranking of No. 49 would suggest. It’s also worth keeping in mind that today saw Tamira Paszek, the defending champion and a quarterfinalist at Wimbledon, retire against Caroline Wozniacki with a left thigh injury, and Agnieszka Radwanska, another former champion and last year’s Wimbledon finalist, beaten by qualifier Jamie Hampton. Backing up one’s achievements is no easy matter in today’s WTA.

“It’s something that I really want—to be there again.” That’s how Kvitova summarizes her feelings when I ask her about Wimbledon during our one-on-one sit-down after the match, and it’s clear that she means more than just playing the tournament. She wants to play like that again; she wants to win. Borrowing my phrase of “ups and downs” to describe her season so far—she won the title in Doha, but has struggled to make much of an impression apart from that, and lost early in Paris and Melbourne—she acknowledges that it’s been “disappointing,” but adds: “…this is the tennis. It’s some[thing] I have to learn.”

Actually, she says “[i]t’s some what I have to learn.” Kvitova’s English has improved a lot (and it’s certainly miles ahead of my grasp of any language other than my own), but it can still be a barrier, such as when I ask her how she feels about male players who criticize equal prize money, She loses herself in a spate of mangled clauses from which it’s impossible to extract a quote, but she still makes her opinion clear: “This is the men,” she shrugs, and laughs.

In fact, Kvitova laughs several times during our conversation—and so do I. She’s funny, in a dry way that hasn’t come across to me before, in little bursts before she settles to the serious business of trying to provide an answer to my questions. When I ask her what it means to her that the WTA is celebrating its 40th anniversary and how she feels about the legendary players who have made women’s tennis is as great as it is, she jokes, “Like me, you mean?” before describing it as “an honor” to be part of the occasion.

Perhaps if we saw more of this Petra, relaxed and amusing, there would be fewer confused spectators trying to figure out who she is. The struggle for players to let the softer, more fun aspects of their personality out for the world to see is a familiar one; Andy Murray’s gradual media evolution comes to mind, as does the recent wholehearted adoption of Twitter by Kvitova’s compatriot and sometime training partner, Tomas Berdych. I ask Kvitova—who is a Tweeter, although a less prolific one than Berdych—if there’s something about who she is as a person that she wished was more generally known. “I think everyone has a personality that they’re trying to show on [the] social networks,” Kvitova says vaguely, and adds, “But sometimes it’s quite tough and hard to open more to the people.” She doesn’t read comments directed to her on Twitter any more, not for about three years, because of the kinds of things that people said. Did it used to upset her? “Sometimes, yes.”

Not all online opinion about Kvitova is unpleasant, though. It was a commenter on this website who coined for Kvitova one of my favorite nicknames of all time, ‘del Petra’, because of the resemblance her big game and placid demeanor bears to a certain Argentine pro. Like Juan Martin del Potro—also a Grand Slam champion who hasn’t yet managed to repeat—the key to Kvitova’s game on this surface is to get low to the ball. Unlike del Potro, she’s played her best tennis on grass.

In the second set against Niculescu, which she wins 6-1, Kvitova starts coming to the net a lot more, slicing beautifully and making delicate drop volleys, managing to outfox the Romanian and, on one memorable occasion, best her in an exchange of reflex volleys. Afterwards, she says with a smile that she’s been practicing volleys so much that “I’m glad that I was there [at the net].”

Like everything Kvitova does, when it works it takes your breath away; when it fails to work, it does so to a degree that makes you wonder how it ever would. It’s a strange alchemy, and I get the sense it’s a mystery she’s still exploring herself. But if it is all going to come together again, there’s no better nor more likely setting for it to do so than on the lawns of Wimbledon.