Abstract: An incremental braking method and system in which a braked member which is in motion, e.g., a brake drum, is engaged by a series of flexible stops on a braking member, e.g., a brake shoe, to brake the braked member. A rigid stop on the braked member sweeps past the flexible stops on the braking member to cause vibrations. The vibrations are damped as the flexible stops engage the braked member, thereby inhibiting the motion of the braked member. The flexible stops are of unequal lengths and are provided on springs which allow them to retract into the braking member. In this way, the stops incrementally engage the braked member for smoother and more efficient braking.