mobile mute, that's what I do esp. when playing with the Jaco-esque tone and can sit it on the pickup bar.

When I work on stuff that involves more string jumping I have to anchor the thumb, though.

This is good though, I'm trying to learn the pinky damping technique, as I bet combining that with some thumb-muting should cover most of the needed bases. I'm pretty young on bass and trying to go at it with even practice on style, chops, and form.