bizarre audio problem

I have a 1995 E36 (i.e. BMW 325) convertible with a completely stock,
non-HK 
stereo, i.e. cassette/radio in the dash and CD changer in the trunk. When
I 
turn it on (radio/cassette/CD - it doesn't matter which) it only plays
from 
the right side speakers until I turn it up to about 60% at which point the

left side speakers start to play. When this happens the volume drops from 
the RH speakers, presumably because some power is now being to the LH 
speakers.

The problem (apart from the fact that I'd like to have stereo even at low 
volumes) is that because it is sending power to only one set of speakers, 
they play much louder, so it is hard to get a required volume level.

Does anyone know what could be the problem and how I would fix it? I want
to 
keep the current (stock) head unit if possible.

Dan