As you probably know, the inside mirror snaps off and on a steel mount that's glued to the glass, and is held more-or-less tight by stiff flat springs built into the mirror base. If you add some rubber thingy between the mirror & the mount, any looseness is 'shimmed out' and most or all the vibration goes away. Just be careful in adding shim materal- if you crack the glued-on mount off the glass, you get to start over!
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