I tried the frame over it, and it does indeed seem like a perfect fit. It's a Sizzix folder, by the way. This was layered up exactly the same as to get the embossed oval with a plain frame: Folder with cardstock, Oval Diffuser on top.
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Use the shim in place of one of the cutting pads in your sandwich, and position it over the panel you want to emboss. The Big Shot only applies pressure to that part of the card stock that has the shim.