A viral illness forced Garbine Muguruza to pull out of the Hobart international but she hopes to be fit for the Australian Open.
Angelique Kerber retired from the Adelaide International due to a back injury, while Marketa Vondrousova thrashed Arina Rodionova.
Anastasia Pavlyuchenkova put up an admirable fight against Ash Barty at the Adelaide International, but the world number one did enough.
Ash Barty shuffered a shock loss in Brisbane but Serena Williams and Naomi Osaka overcame scares ahead of the Australian Open.
Former Wimbledon runner-up Eugenie Bouchard has fallen outside the world's top 250 but showed a hint of past form with a fine Auckland win.
Serena Williams starts the 2020s on the brink of a record-equalling 24th major, while the battle to be the leading man is very much on.
Garbine Muguruza has turned to Conchita Martinez in a bid to return to the peak of her powers after splitting with Sam Sumyk.
Returning to the scene of her maiden grand slam title, world number one Naomi Osaka outlasted Anna Blinkova in three sets on Tuesday.
Venus Williams upset Kiki Bertens as five seeds fell at the Western & Southern Open.
Former French Open and Wimbledon champion Garbine Muguruza will look to address her recent slide with a change of coach.