A poor mans string dampener can be one of those thick asses pony tail holders.

Or better yet...Michael Angelo sells one on his site although a bit pricey:
http://www.angelo.com/products_1.html#stringdampener
pics of it in use:
http://www.angelo.com/photo_gallery_9.html#Dblegtr

When I attended G.I.T. from 94 to 95..Roy Ashen one of my teachers there who tought the 8 finger tapping technique used a ponytail holder (The girly looking thick kind). He's even used a sock tied lightly around the first fret area.