Thanks klearview - I think you nailed it. Except that there is a key /schemas/apps/nautilus/desktop/volumes_visible which I think is overriding my change to volumes_visible as you described. I get the message "Currently pairs and schemas can't be edited. This will be changed in a later version." when I try to change the schema key and the volume icons remain :-((
I did disappear the trashbin icon from the desktop some time back however, I do not remember how.