Jessica Pegula is the Hologic WTA Tour’s No.3-ranked player and has advanced to four of the past five major quarterfinals. And yet, a champion’s ability to finish -- to power through the back end of tournaments -- remains a work in progress.

Yes, Pegula broke through last October as the winner of the Guadalajara 1000, beating some formidable players. But it was only the second WTA title of her career. Pegula, who turned 29 last month, is playing her best tennis in what, for many players, is a relatively late stage. What does she need to do to get to the next level?

Pegula saves two match points to win late-night thriller in Miami

Pegula, an extremely self-aware person, started nodding before the entire (and lengthy) question was even out of a reporter’s mouth earlier this month at Indian Wells.

“I would definitely like to go further in a Slam or just start winning more tournaments,” she said. “It’s kind of a little bit of everything, the margins become very small. At the same time you don’t need to change your game, but I think just fine-tuning things.”

Thursday’s semifinal at the Miami Open presents Pegula with precisely the kind of opportunity she’s talking about. The No.3 seed faces No.10 Elena Rybakina, an in-form 23-year-old from Kazakhstan.

Rybakina already won Wimbledon a year ago and, most recently, Indian Wells -- but Pegula holds a 2-0 head-to-head edge. Pegula won a Miami third-round match last year in straight sets. On the way to the title in Guadalajara, Pegula was pushed to three sets only once, by Rybakina, who failed to convert three match points and fell in a taut 10-8 tiebreak.

“I think she and [Aryna] Sabalenka are the ones to beat right now,” Pegula said of Rybakina, “so it’s going to be a great test and a deserved semi for a tournament like this.”

Pegula is not blessed with the easy power of Rybakina or the sheer athleticism of Iga Swiatek, Sabalenka or Coco Gauff. Instead, she’s made herself into a terrific all-around player, with brisk, flat groundstrokes and the hands of a doubles specialist. Interestingly, she’s won six doubles titles, tripling her singles crowns.

"She doesn't have spectacular strength or she doesn't do much fuss about whatever she's doing, she's not screaming," said Magda Linette, who bowed out to Pegula in the Round of 16.

"But the timing that she has, the easiness that she's hitting with, and the power that she can generate just because of how well she times the ball, it's special. I find her extremely talented and really smart on court. You can see she reads the game, she knows what she's doing and she trusts her shots. I don't think she gets the credit that she really deserves."

One of coach David Witt’s initiatives for Pegula is to squeeze a few more miles per hour out of her serve. Typically, she’s clocked in the middle of the pack, around 100 mph on average for a first serve.

“I’ve definitely been serving I think a little bit bigger,” Pegula said. “Getting some more free points on my serve always helps.”

Movement is another area of concentration.

“Because,” she said, smiling, “I’m not the most natural mover -- not like a Coco or Iga. I’m always working on that.”

More so, to challenge the best, Pegula needs to play more aggressively and come out of her comfort zone.

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“Against the bigger hitters, I’ve got to be able to take my chances and move forward,” Pegula said. “Then just working on implementing little things in my game and still trying to play aggressive.”

This is Pegula’s second straight visit to the Miami semifinals. It was also her 12th quarterfinal at a WTA 1000, the most among WTA Tour players over the past three-plus years. Her consistency is laudable, but she’s hoping to conjure more matches like the 6-2, 6-2 stunner of top-ranked Swiatek back in January at the United Cup.

“I played a pretty flawless match, to be honest,” Pegula said. “I think it helps just knowing what I have to do to win, knowing what worked, what didn’t work. I kind of did everything I wanted to do was just working.”

She’ll need to feel that vibe again Thursday against Rybakina.