Ledger's relationship with the press in Australia was sometimes turbulent, and it led to his abandonment of plans for his family to reside part-time in Sydney. In 2004, he strongly denied press reports alleging that "he spat at journalists on the Sydney set of the film Candy", or that one of his relatives had done so later, outside Ledger's Sydney home. On 13 January 2006, "Several members of the paparazzi retaliated ... squirting Ledger and Williams with water pistols on the red carpet at the Sydney premiere of Brokeback Mountain".
From 2000 to 2005, he starred in supporting roles as Gabriel Martin, the eldest son of Benjamin Martin (Mel Gibson), in The Patriot (2000), and as Sonny Grotowski, the son of Hank Grotowski (Billy Bob Thornton), in Monster's Ball (2001); and in leading or title roles in A Knight's Tale (2001), The Four Feathers (2002), The Order (2003), Ned Kelly (2003), Casanova (2005), The Brothers Grimm (2005), and Lords of Dogtown (2005). In 2001, he won a ShoWest Award as "Male Star of Tomorrow".
After Brokeback Mountain, Ledger costarred with fellow Australian Abbie Cornish in the 2006 Australian film Candy, an adaptation of the 1998 novel Candy: A Novel of Love and Addiction, as young heroin addicts in love attempting to break free of their addiction, whose mentor is played by Geoffrey Rush; for his performance as sometime poet Dan, Ledger was nominated for three "Best Actor" awards, including one of the Film Critics Circle of Australia Awards, which both Cornish and Rush won in their categories. Shortly after the release of Candy, Ledger was invited to join the Academy of Motion Picture Arts and Sciences. As one of six actors embodying different aspects of the life of Bob Dylan in the 2007 film I'm Not There, directed by Todd Haynes, Ledger "won praise for his portrayal of 'Robbie [Clark],' a moody, counter-culture actor who represents the romanticist side of Dylan, but says accolades are never his motivation". Posthumously, on 23 February 2008, he shared the 2007 Independent Spirit Robert Altman Award with the rest of the film's ensemble cast, its director, and its casting director.