Bagginsbill, I tried out your suggestions. I have Poser 7, so I raised the reflection value. With about 1,25 it looks better(lighter) and white reflected objects don't get overexposed.

Thinking of your point about rendering without lights, I tried to lighten the background of the reflection with clouds (image above). This may look right in some situations. But the blue and white objects were still too dark. So I removed the clouds and put a backlight between mirror and objects and pointed it at a flattened (invisible) cylinder, that cuts through the objects. This lights up the whole mirror not only the reflection, but I will try this out with a full scene.
Thanks again for your help. Till now I mostly solved problems the quick and dirty way, very often in postwork, but this waked up my ambitions to wrestle more out of the Poser features and out of me.