Katie Boulter was among three Britons to win on Tuesday in the first round of qualifying for next week's Australian Open but Liam Broady lost in Melbourne.
Boulter edged out American Caroline Dolehide 6-3 3-6 7-6 (10-5).
Lily Miyazaki beat American Hailey Baptiste 6-4 7-5, with Jodie Burrage easing past Elysia Bolton of Australia 6-2 6-4.
But Broady was defeated 6-3 6-7 (4-7) 7-6 (10-7) by Ecuador's Emilio Gomez after a near three-hour battle.
Katie Swan lost to France's Jessika Ponchet and fellow Briton Ryan Peniston was beaten by Canadian Alexis Galarneau.
Miyazaki will take on Jang Su-jeong of South Korea in the second round of qualifying on Wednesday.
Burrage faces Czech Barbora Palicova later on the same day, with Boulter playing Russian teenager Polina Kudermetova.
Elsewhere in the women's singles qualifiers, Czech teenager Linda Noskova, finalist at this year's Adelaide International 1, suffered a shock defeat by Canadian Katherine Sebov.
Britons Harriet Dart and Emma Raducanu are already in the women's singles main draw, although 2021 US Open champion Raducanu is still recovering from an ankle injury.
Cameron Norrie, Dan Evans, Kyle Edmund, Andy Murray and Jack Draper are in the main draw of the men's singles at the opening Grand Slam of the year, which begins on Monday.