Katie Boulter, Lily Miyazaki and Jodie Burrage won in the first round of qualifying for next week's Australian Open but two other Britons were defeated in Melbourne.
Miyazaki beat American Hailey Baptiste 6-4 7-5, with Burrage easing past Elysia Bolton of Australia 6-2 6-4.
But Katie Swan lost to France's Jessika Ponchet and Ryan Peniston was beaten by Canadian Alexis Galarneau.
Fellow Briton Liam Broady faces Ecuador's Emilio Gomez later on Tuesday.
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.