Finally driven mad by the rattle from my Klick Fix map holder yesterday on a 200k audax (and for me that's a long time to be driven mad) I gave it some thought and came up with this instead of the big hammer. Might be of interest to others with the same affliction.
Strip the black plastic body and using a 1/8" strip of old inner tube (what else!) stretch it between the two plastic lugs and reassemble. Photos do a better job of explanation.
Must get a life, must get a life..
