After the childless Rubbles wish upon a star for a baby of their own, Barney finds a basket containing the world's strongest foundling. However, someone else wants to adopt little Bamm-Bamm, and he's rich.

Betty and Barney discover a foundling named Bamm-Bamm on their doorstep and become smitten with the child. They set out to adopt him, but discover that the Welfare Bureau has promised the boy to wealthy Pronto Berger, who is being represented by attorney Perry Masonry. When Berger learns that his wife is pregnant, however, the Rubbles are free to adopt the baby.