Try to find yourself a used Jerry Jones Longhorn semi hollow bass, as they are not in production anymore.
They are high quality versions of Danelectro's Longhorn basses.
I owned one ones, kind of regret selling it too, since it was really nice to play on and had a fantastic sound, and even a lot of sound variation possibilities, at least, beside the volume control, mine came with a tone control and a 4 way pickup switch that made you able to chose, bridge, neck, bridge+neck serial, bridge+neck parallel.
It seems though that some models only have volume, tone and a three way pickup switch.
Anyway, that would be my recommendation, hands down, in every case someone needs a semi/hollow body short scale bass.