RT found an interesting article in which Katherine Hopwood-Poulsen, a vocal coach who specialises in American dialects, reviews some of the most popular Australian actors’ American accents. What she says about Rose Byrne:

‘Everything is there. The sounds, the connection to the thoughts and the placement in the mouth.’ Byrne is so relaxed that Hopwood-Poulsen believes she no longer has to think about the accent. ‘Look at her,’ she says. ”Not a trace of tension. The accent is so much a part of her you don’t even realise she’s doing one. Her focus is entirely on the character, the dialogue and the emotion.

Source and full article Thanks RT.