If you are damping a thin-wall enclosure then the thickness will be very important.
Using too little will prove pointless as it won't have the desired effect of both lowering panel resonance and damping it.
World Designs sell rolls of damping material similar to that mentioned by Simon.
Works well IME and isn't expensive.
Check out the BBC Research Depatment archive for the papers relating to the LS models.
These give valuable advice on cabinet construction and damping, including the choice of material and application.
With regard to reducing internal volume, it is worth noting that the maximum damping benefit is obtained by placing the material in the centre of the panel. Little benefit is obtained by extending out to the edges which are more effectively clamped by the enclosure construction.