The following year she was nominated for a Best Supporting Actress Oscar for the role of a mother whose child is abducted by aliens in Steven Spielberg's "Close Encounters of the Third Kind". That same year, she made an uncredited cameo in "The Muppet Movie" and had a role in the comedy "Slap Shot" with Paul Newman. Four years later, Dillon was again nominated for a Best Supporting Actress Oscar for her performance as a suicidal teacher in "Absence of Malice" in 1981, working again with Newman.