Edward Raymond Müller (June 23, 1911 – April 8, 1991) was a jazz musician who played tenor saxophone and clarinet born in New Orleans, Louisiana.
His professional career began in New Orleans at 16 with his recording debut occurring in 1930. He worked in Ben Pollack's orchestra and then with Bob Crosby. He stayed with Crosby until the band broke up in 1942. He had his own band for a brief time after that before being drafted. However, he was discharged from the military early because of illness and settled in Los Angeles. After that he worked with Pete Fountain, appeared in most of Crosby's reunions, and did club work. Eddie also played with trumpeter Al Hirt.
Miller was also a songwriter with his best known song being "Slow Mood," later known as "Lazy Mood" after Johnny Mercer noticed the tune and composed lyrics. Miller was inducted into the Big Band and Jazz Hall of Fame in 1998.