In New Orleans in 1944, William Russell recorded a small jazz combo with George Lewis and Jim Robinson for his American Music label.
Robinson cut loose with an unexpectedly virtuosic performance on an instrumental of the tune "Ice Cream".
When Barber's band first recorded the song in 1954, they basically knew the instrumental Lewis version.
The record producer asked them to sing it, which was slightly problematic, since they didn't know the full lyrics.
So trumpeter Pat Halcox invented his own lyrics; these are nowadays better known than the original 1920s version.