I'm working on this to cut down on travel for especially fast parts. I play 6 strings and typically rest my thumb on the B string, unless there is a fast part on a string other than E, in which case I will move my thumb to the string below it for rest (for instance, if I'm doing the Dream Theater bass solo in "Dance of Eternity," I move my thumb from the B string to the E string and start the solo on the A and reach from the E - it's a lot easier than playing the whole thing from the B). If I'm playing something fast on the D string, I rest my thumb on A. Cutting back on travel has made a HUGE difference in endurance and speed in playing.
Bassist for Chaometry * ESP Club - 102 * MIDI/Bass Pedals Club - 6 * Progressive Rock Club - 1 * Fretless Club - 403 * Team Trace Elliot - 169 * LGBT Bass Players Club - 17