Compton was born in Harrodsburg, Kentucky, and is first recorded as a pianist and entertainer in Louisville in about 1904.
That year, he met pianist Tony Jackson, collaborating with him in writing a piece, "The Clock of Time", which was reportedly re-used as the basis of the 1922 song "My Daddy Rocks Me (With One Steady Roll)", recorded by Trixie Smith with a writing credit to music publisher J. Berni Barbour.
He worked with composer Shelton Brooks, who dedicated his 1916 piece "Walkin' the Dog" to Compton.
He also performed in San Francisco, where he met and worked with Jelly Roll Morton, Florence Mills, and Ada "Bricktop" Smith.
He returned to work in New York during this period, making his final trip to perform in Paris in 1939.