Top seeds Carlos Alcaraz and Daniil Medvedev made strong starts to the Shanghai Masters on Saturday, both winning in straight sets to sail through to the third round.
Italy's Jannik Sinner is also through after battling out an intense first set -- saving four set points -- against the United States' Marcos Giron.
Alcaraz dominated his first set against 73rd-ranked Gregoire Barrere, winning it 6-2.
But the Frenchman regained ground in the second, sending 20-year-old Alcaraz scurrying from side to side of the court.
The world number two kept his cool and drew ahead towards the set's end, finishing it off at 7-5.
"There were no ups and downs on my game," said Alcaraz when asked what had pleased him the most about his performance.
"I just stayed at the same level all the time. (Barrere) increased his level, but... my level of focus was all the time the same."
Steady play may have been preoccupying the Spaniard after he said he went "out of his mind" during his defeat at the hands of Sinner at the China Open in Beijing this week.
The loss dealt a blow to his plan to close the gap on the absent Novak Djokovic at the top of the rankings with strong performances in China.
Asked whether he was more worried about meeting Sinner again or Medvedev later in the tournament, Alcaraz laughed.
"That's a tough one. Both of them," he said.
"It's scary to face them... but I like that kind of challenge," he added.
"I want to play my best level to make the final and probably face them."
- Lucky butterfly -
Medvedev, the world number three and defending champion, beat Chile's Cristian Garin in straight sets 6-3, 6-3 to proceed breezily to the third round.
Garin put up a valiant defence, with several hard-fought rallies inducing gasps from the crowd, but ultimately the 98th-ranked player struggled with the Russian's relentless pace.
"(There's a) long tournament ahead, with a lot of strong players, starting from my next match," said Medvedev at the end.
"But the goal for sure is to try and win this beautiful trophy one more time."
Medvedev won the 2019 title, but for the next three years the tournament was cancelled because of the Covid-19 pandemic.
"I'm definitely happy to be back in Shanghai," he said. "I honestly feel great and I want to stay here as long as possible."
Medvedev is popular with Chinese fans, a chemistry on display when the indoor match was interrupted briefly after a red-and-white butterfly distracted the Russian from serving.
The crowd giggled as he played up his surprise for comic effect, before carefully handing over the insect, which had settled on one of his tennis balls, to great applause.
"I'm a little bit, not scared of insects, but, like, I don't like when they go on me," Medvedev said at a press conference afterwards, though he added it was "perfect for me" upon hearing they were a symbol of good luck in China.
The Russian plays again on Sunday against 26th-ranked Sebastian Korda, who beat him at their last meeting.
"He was very dominant, in a way, and that's how he plays, so it's going to be interesting for me," said Medvedev.
- Sinner prevails -
Sinner, who also defeated Medvedev on his way to winning the China Open this week, had a more challenging route to the third round in his Shanghai Masters debut.
The world number four snatched a nail-biting first set 7-6 (9/7), before coming back strong in the second set for a quick 6-2 victory.
"(Giron) is a very, very good player... The first set is never easy, I got lucky a little bit but sometimes you need a bit of luck," Sinner said after the match.
"In the second set I was able to raise the level a bit... so I'm very happy with that."
Sinner will face Argentina's Sebastian Baez on Sunday.
Fourth seed Stefanos Tsitsipas is also through to the next round after a straightforward job dispatching Australian qualifier Rinky Hijikata 6-4, 6-2.
And world number eight Taylor Fritz progressed after a gruelling three sets against Japan's 79th-ranked Yosuke Watanuki, winning 7-6 (7/2), 6-7 (6/8), 6-4.
Several other second-round matches were suspended on Saturday because of rain.
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