Caroline Wozniacki won through to the second round of the Sydney International after battling past Monica Puig and top seed Kiki Bertens wasted no time in winning her first-round match at the Hobart International on Monday.
Wozniacki finished 2016 strongly, but the former world number one's hopes of starting this year with a tournament victory were ended by Julia Goerges at the quarter-final stage in Auckland last week.
The Dane came through a battle with Olympic champion Puig on day two of the tournament in Australia, recovering from a second-set wobble to prevail 6-3 2-6 6-4.
Puig was looking for her first victory of the season and responded to losing the first set by winning the first four games of the second before going on to level the match, but paid the price for failing to hold in the first game of the decider.
WTA Finals champion Dominika Cibulkova made a statement, outclassing Laura Siegemund 6-2 6-0, while sixth seed Johanna Konta saw off Arina Rodionova in straight sets.
Coco Vandeweghe was leading eighth seed Elena Vesnina 6-2 4-0 when the Russian retired, while Daria Gavrilova advanced in her homeland along with Roberta Vinci, Christina Mchale, Barbora Strycova, Anastasia Pavlyuchenkova and Duan Ying-ying.
Bertens needed just 68 minutes to breeze through in Hobart, where Annika Beck was soundly beaten 6-1 6-2.
There were seven breaks for the world number 22 from Netherlands in a one-sided match as Beck failed to do herself justice.
Seventh seed Kristina Mladenovic bowed out after she was hammered 6-1 6-2 by Elise Mertens on a day which saw the likes of Johanna Larsson, Lucie Safarova, Lara Arruabarrena and Kirsten Flipkens progress.