Naomi Osaka showed plenty of encouraging signs as she went down in two tight sets to Caroline Garcia on her return to the Australian Open stage.
France's great home hope, Caroline Garcia, was bundled out of Roland Garros in the second round after a dramatic encounter with Russian Anna Blinkova.
Fifth seed Caroline Garcia and sixth seed Coco Cauff both came unstuck at the Madrid Open on Saturday, though No 2 seed Aryna Sabalenka had no such problems.
Aryna Sabalenka says she has Iga Swiatek's World No 1 ranking firmly in her sights after easing into the third round of the Miami Open on Friday.
Aryna Sabalenka gave a statement of her intent at the Australian Open by powering past Belinda Bencic to reach the quarter-finals.
Tunisian star Ons Jabeur battled to a three-set victory over Tamara Zidansek in the first round of the Australian Open.