Based on the lullaby Hush Little Baby, this was written by the brother and sister duo Inez and Charlie Foxx (their real names) and released in 1963. It reached No 7 in the US but did not make the charts in the UK until it was re-released in 1969, when it got to No 33.
Dusty Springfield recorded it for her debut solo album A Girl Called Dusty in 1964. She sang both parts.
This is a live performance from 1965. I believe the backing group are the Echoes. As far as I can tell they were an instrumental line-up and I don’t know who is the vocalist on this one.
In one of the less likely match-ups in pop history, Dusty and Jimi Hendrix performed the song on a 1968 episode of her ITV variety show, It Must Be Dusty. This fragmentary video confirms that it happened.
Carly Simon and James Taylor recorded the song for her 1974 album Hotcakes. Released as a single, it made No 5 in the US and No 34 in Britain.
Here is a live performance from 1979 which was released on the album No Nukes: The Muse Concerts For a Non-Nuclear Future.