This work examines how friction-induced oscillations in a traditional mass-on-a-moving-belt system are affected by high-frequency excitations, commonly referred to as dither signals. Two different friction laws are considered: a Stribeck friction law governed by a relationship that is cubic in the slip velocity, and an exponentially-based friction law that steadily decreases with slip velocity. Although in both cases the friction force has an initial negative slope versus relative velocity, their stability characteristics are quite different. In particular, it is shown that tangential dither can either stabilize or destabilize an initially stable system, depending on the nature of the friction law, and on other system and dither parameters. The behavior of the systems is studied through use of an averaging technique and through direct numerical simulation. The numerical study validates the stability predictions from the averaging method, and quantifies the partial-cancellation performance of tangential dither.