The Ikettes provided the backing vocals (uncredited on the single). And although the single was officially produced by »Ike and Tina Turner«, on its label we read only »Fontella Bass with Oliver Sain Orchestra«:
Fontella Bass (feat. The Ikettes): »My Good Loving« (Prann # 5005A):
Tina Turner herself. However, Tina only sings on the A-side »Poor Little Fool« which is why the billing on the label says »Fontella Bass and Tina Turner«. On the B-side, »This Would Make Me Happy«, there is only the voice of Fontella. In any case, Tina's contribution to »Poor Little Fool« is limited to the melodical main part of the song: »Poor little fool, why can't you see / This romance will never be«. In this part she accompanies Fontella in what is basically a close-harmony-duet. Yet the song is remarkable not only for being a fine, bluesy r&b-ballad, but also for being the only recording from the 1960s, as far as I know, where you can hear Tina Turner together with another female singer (apart from the Ikettes, of course). And yes, in general Tina was not used to playing the second fiddle ...
Fontella Bass (feat. Tina Turner*);
»Poor Little Fool*« / »This Would Make Me Happy« from Vesuvius # 1002 (1963):
Some discographies list Vesuvius # 1002 as a recording (and, consequently, as a release) from 1964. According to most of the information I have this is not correct, but on the other hand, information is scarce regarding this 45. So maybe 1964 it is. We gonna find out some day.
POSTSCRIPT Oct. 17, 2011
There is now an enthusiastic review of »Poor Little Fool« over at Voyager's World. Check it out!