I've been doing more research. The story from the Arabian Nights
about the Pari is "Prince Ahmed and Fairy Pari-Banou." One source
said that paries are djinnis. But most sources affirm that djinnis
are all ugly and evil. Paries, as I wrote before, are beautiful
females, who, in atonement for their fallen angel ancestors, lead
mortals to the isle of the blessed, to Paradise (Pari-dise?)

I think I Dream of Jeannie was a composite of the Prince Ahmed story
and Aladdin, which is also in the Arabian Nights.

Paries are made of fire, and sustain themselves on perfume (remember
the episode where tony and jeannie trapped jeannie's sister with
perfume?) Demons like to capture paries, and put them in cages, which
they hang from treetops. Other paries keep the trapped pari alive
with perfume.

Oh, BTW: djinnis were controlled by Solomon, not because he
controlled their bottles, but because he designed rings which had
magical powers over them.

Tom