Morton's next major role, the pivotal part of Hattie in Sweet and Lowdown (1999), resulted in critical raves and an Academy Award nomination for Best Supporting Actress.
Further accolades came her way for her portrayal of a junkie in Jesus' Son (1999) and the psychic Agatha in director Steven Spielberg's Minority Report (2002). Cast as a young Irish mother in director Jim Sheridan's In America (2002), Morton earned a Best Actress Oscar nod. She received her first Emmy and BAFTA TV nominations for her role as a convicted murderer in the TV movie Longford.