Dan, Rattling is not inherent in the "classic" bridge design, but is in the roller bridge on the C58 and C64. Those bridges were used for authenticity.
In the non-roller type of classic bridge, the most common causes are badly-adjusted height screws, and loose saddles. The roller bridges have the same basic design (with rollers added, of course).
Once the height of the bridge is established during setup, care must be taken to ensure that the bridge is sitting level (front to back) and that each pair of height-adjusting Allen screws contacts the bridge base plate. Because the strings apply downward pressure on the entire bridge, it's possible for the bridge to stay in place without all four of the screws contacting the baseplate solidly and with equal force. I've set up more than one Rick guitar which had one of the four screws absent. So, once the height has been adjusted for both bass and treble sides, make sure that the two screws on each side meet resistance when gently turned with the Allen adjusting wrench. If either screw is loose, just snug it up enough to contact the plate. Too much tightening and you raise the bridge a smidge, and then the other screw needs tightening, which could again raise the bridge infinitesimally, and so on, etc.
These screws can vibrate out of adjustment. Over the years, both rubber "O" rings and short springs have been used in an attempt to minimize this, but the best solution I've found is to use a touch (with a toothpick) of red LocTite (Product # 271):
http://www.loctiteproducts.com/products ... 8&plid=154
Too much of this, however, is NOT a good thing. Get the bridge set up exactly as you want it, and apply a small drop with a toothpick, making sure it flows into the threads.
The second cause of buzzing is loose saddles. The saddles are made of alloy sheet, and need to fit tightly against the bottom bridge stamping, so they do not rock. It's the rocking from side to side that causes buzzing. The most common fix for this is to cut a tiny (1/4" X 1/4" or so) piece of brass shim stock of an appropriate thickness to wedge under the saddle so it doesn't rock. Generally, the bridge (or at least the offending string) must be removed to accomplish this fix satisfactorily.
Brass shim stock can be bought from the K & S Engineering rack display at hobby and hardware stores and home centers.