Simona Halep and Petra Kvitova both won their opening matches at the Dubai Championships on Tuesday, while Elina Svitolina made a strong start to her bid for a third straight title.
Kvitova, the 2013 winner, recovered from losing a first-set tiebreak to defeat Katerina Siniakova 6-7 (3/7), 6-4, 6-4 and squeeze into the third round.
Halep, Dubai champion in 2015, saw off 2014 Wimbledon finalist Eugenie Bouchard 7-6 (7/4), 6-4.
The Romanian said she is still feeling the effects of her weekend final defeat in Doha by Elise Mertens.
"It was a good match because I won it. I tried to finish the points faster because I'm a little bit tired," Halep said.
"She played well, the level was pretty good. At some points I really ran very well. I'm confident. I feel good on court even if I'm tired."
A third former world number one also advanced as Angelique Kerber beat Dalila Jakupovic 7-6 (7/4), 6-3.
Kvitova, Wimbledon champion in 2011 and 2014, said she was unfazed about the early midday start to her match.
"I don't really care if I play the first match," the Australian Open runner-up said. "Now I'm done, so I have a free afternoon.
"I'm not sure what I'm pleased with... maybe with my comeback at the end.
"Even when I lost the tie-break, I was really fighting in the first set to get it done, then the tie-break was just a little bad from my side.
"I won my first two games in the second set. It was really helpful for me mentally. That's probably what I'm pleased with."
Svitolina benefits from Jabeur injury
Local favourite Ons Jabeur was forced to retire with the Tunisian trailing Svitolina 7-6 (7/4), 4-0.
Jabeur took a fall late in the opening set, rolling her ankle while also hitting her shoulder.
She took a medical timeout out but was only able to carry on in the second set for four games.
Third seed Svitolina is hoping to become the first women to win three Dubai titles.
"That is a big motivation for me here," the Ukrainian said. "Today I didn't really feel in a match mood, I don't know why.
"I was struggling a bit, I had a very slow start. Hopefully tomorrow will be better.
"I told myself that I'm here to make history of the tournament."
Elsewhere, Hsieh Su-Wei defeated Belarusian Aliaksandra Sasnovich 6-1, 6-2 while Viktoria Kuzmova accounted for seventh seed Kiki Bertens, beating this month's St Petersburg champion 6-2, 4-6, 7-6 (8/6).
American Jennifer Brady downed French 14th seed Caroline Garcia 6-4, 7-5 as her compatriot Sofia Kenin defeated Russian 11th seed Daria Kasatkina 6-3, 2-6, 6-4.
A third US player, Alison Riske, advanced 6-2, 6-3 over Alize Cornet.
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