The problem with acoustic attenuation of your tweeter's output is that any material absorptive enough to make a significant differnce down at the bottom end of your tweeter's range is going to be overly absorptive in the top octave.
Assuming were talking about the Sarastros, I would consider experimenting with maybe one inch thick open-cell foam along either side of the tweeter, cut so that the sides are V-shaped, sort of like the faceplate's angle around the tweeter diaphragm. The idea is to allow the tweeter to output unimpeded across a reasonably wide arc (maybe 90 degrees or so), and then attenuate its output beyond that arc. We want the foam to be thick enough that it will effectively attenuate energy at the lower end of the tweeter's range. I really don't know if this will work or not, and several tries would probably be necessary to fine-tune if the initial try is promising, but I think this has a better chance of making a net improvement than placing absorptive material in front of the tweeter.
Duke
dealer/manufacturer