"Rich Woman" is a song written by Dorothy LaBostrie and McKinley "Li'l" Millet, who recorded it in 1955; and was most notably recorded by Robert Plant and Alison Krauss on their 2007 album Raising Sand.

The song was first recorded by Li'l Millet and his Creoles, for Specialty Records. He co-wrote the song with LaBostrie, who had previously co-written "Tutti-Frutti" with Little Richard. It was produced by legendary New Orleans producer Robert Blackwell. It was recorded at Cosimo's J&M Studios in September, 1955, and released in November 1955. Backing musicians on the sessions were Edgar Myles (vocals, trombone), McKinley "Li'l" Millet (vocals, bass), Lee Allen (tenor sax), Ernest Mare (guitar), Bartholomew Smith (drums), James Victor Lewis (tenor sax) and Warren Myles (piano).

Canned Heat recorded it for their eponymous first album, in 1967, on Liberty Records.

The Fabulous Thunderbirds included it on their eponymous first album (also known as Girls Go Wild) in 1979, on Chrysalis Records.

Robert Plant & Alison Krauss opened their 2007 album Raising Sand with their version of the song.

Boz Scaggs opened his 2015 album A Fool To Care, with his version on the indie label, 429 Records. His version most closely resembles the Li'l Millet original.

...
Wikipedia