Fan feels loose, should I add a shim?

As shown below, I have a Norhtwood P4 and a Volcano 7+ HSF, but if i grab the heatsink while installed, it seems slightly loose. Should I take off the heatsink and add a 1.5" x 1.5" thin piece of copper? (with ATC3 on both sides)

I wouldn't add a shim on top of the cpu I would look somewhere else to take up the space. Do you have to change the bottom piece with that HS?? Add a shim only if you gotta.. It can twist but it must be pressing tightly on the cpu.

I had one of these on my Th711 and took it off and stuffed it in a box in my closet! The way those clamps work they put most of the pressure along the centerline of the heat sink, alowing it to rock side to side. When I'd take it off to change the cpu, do a wire wrap or what ever, I'd always find that the contact patch impression in the as3 was never even.
I bought a Zalman and I'm happy with it, but most people here prefer a thermalright or swiftec I think.