I would like it to be quite short (less than 30cm/12in) or
be able to fold it somehow, so that I can park my car (SUV) in the
basement.

Tho not always true, "short" and "good performance" rarely go hand in hand. If
you're willing to fold over, look at the Comet SB15 or the Diamond equiv....my
SB15 has around 100K miles on it, works great, excellent performance (both FM
and SSB) for a vertical and folds over for those nasty parking decks. Ford was
SO nice to put in an antenna holder on their SUVs (company vehicle)....it is
called the rear window wiper....

Now, to get the wife to allow me to put one on the new Mini....with a
screwdriver on the other side. Hmmm, think the ATAS120 might
work...mini-screwdriver for a Mini.....

A