One often hears that overspun strings sustains too long, compared with gut strings.
Thus it seems strange that I've never seen anyone damp overspun strings with foam rubber. Is is easy to control the amount of damping by using dampers of different sizes, or by sliding dampers farther or closer to the bridge. Strings damped this way don't sound like gut, but for some pieces I find them a significant improvement. If you're lucky enough to have yellow foam rubber instead of pink, the dampers will match the soundboard rather well. Alternatively, there are also opportune times, notably at the end of pieces, when you can damp a string with your thumb to good effect. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
