OK, I've figured out the location of the maddening buzz inside my '04 Cooper. It's coming from the base of the right-hand sun visor. Probably can be fixed by taking down the visor and doing some lubricating, insulating, or tweaking on the inside of that base. The thing seems to be attached to the roof by two screws, and they are shielded by two plastic covers. And the problem is I can't get those covers off. There is no notch to insert a prying tool, and the rim space is too tight for any screwdriver or blade in my (limited) arsenal. This seems like a pretty silly roadblock. What's the answer for popping off those little covers?

Apologies for such a basic question in the technical forum, but I'm sure somebody here can set this klutz on the right road.

John

 

They do just lift out... I removed my visors for cleaning and removing the warning stickers when I got my '04 MINI..

One trick that I did was to use a flat tooth pick (or a very small flat blade screwdriver) to push between the cover and the outer plastic frame. Then when the point is below the surface pry it up slowly... I think there is a little retaining bump on the pointed end of the cap so start on one of the sides..
If you do happen to make any marks on the cap it will be out of view when replaced.. to replace the cap they will just push straight back in.

Perhaps once you tighten down the screw heads your buzz will go away.. Becareful not to over tighten, I think those screws thread in to a plastic nut.

Good luck..