Make Me Your Baby (1965)

Written by Helen Miller and Roger Atkins.

O: The Pixies Three 1965  Cameo Parkway (released 2001)

C: Barbara Lewis 1965 Atlantic

So the Original is on this album. 

From Wikipedia, Yahoo Groups and other sites:

The demo for "Make Me Your Baby" was cut by journeyman session singer Jean Thomas on 22 January 1965 at the behest of Atlantic Records president Jerry Wexler, who wanted to offer the song to Patti LaBelle and the Bluebelles, then a Cameo-Parkway act Wexler was hoping to woo over to Atlantic.

Roger Atkins, one of te writers had the demo made by Jean Thomas, but it was destroyed in the 80-'s when his house was flooded.

An other "demo" we find on an album called "Before they were Hits - Vol. 3". I found this about that recording:
"It seems the demo I picked up last year of *Make Me
Your Baby* that I was reliably informed was by Jean
Thomas is in fact a 1972 remake demo by Donna Marie
(as Tracy Russell). I didn't dub the track from
original acetate and after corresponding with Donna
it is now apparent that the demo is her work."

So that "demo" was made seven year after the song was done by Barbara Lewis. Even the co-writer Roger Atkins didn't know about that demo and he doesn't understand why it was made.

Back to 1965:

Although Patti LaBelle and the Bluebelles did sign with Atlantic, "Make Me Your Baby" was still unrecorded in the summer of 1965 when the success of "Baby I'm Yours" alerted Wexler to the suitability of "Make Me Your Baby" as a vehicle for its singer, Barbara Lewis. She recorded the song at Atlantic Recording Studios in New York City on July 1 1965. Like "Baby I'm Yours", it was produced by Ollie McLaughlin and Bert Berns - being described as "An Ollie McLaughlin production directed by Bert Berns" - and featured George "Teacho" Wilson conducting his orchestra. The arranger was Artie Butler. The song was released in September 1965 and that November matched the #11 peak of her preceding hit, "Baby I'm Yours".

Prior to the release of the Barbara Lewis version, the song had been recorded by the Pixies Three, whose version had successfully been pitched to Cameo Parkway. However, before the relevant contract had been finalized, the Barbara Lewis single had begun to break, causing Cameo Parkway to opt out. The Pixies Three consequently disbanded.

The recording of "the Pixies Three" is released in 2001 on the album "Our History"

Barbara Lewis' "Make Me Your Baby" had an unsuccessful September 1965 release in the UK, where a local cover was cut by producer Shel Talmy with vocalist Liz Shelley. Released 10 September 1965 on Brunswick, this version also failed to chart, but, despite the advance of Lewis' version on the US charts, Shelley's single was given an American release by Decca Records.

Bobby Vinton remade the song as "I'll Make You My Baby". Billy Sherrill produced the track which, as the lead single for the Ev'ry Day of My Life, reached #30 on the Easy Listening chart in Billboard in April 1971, just missing the Billboard Hot 100 by peaking at #101 on the Bubbling Under chart.

"Make Me Your Baby" was covered in late 1975 in a disco style by Canadian singer Suzanne Stevens. Her version reached #23 on Canada's RPM singles chart in December, 1975. Lewis' version had reached the top 10 in Canada in late 1965.

Lewis's original version appeared on the soundtrack of Michael Apted's Stardust.

 Here is the hitsingle

 

Here a video of Barbara Lewis

You can get them if you really want.