Programmable-gain amplifier systems are provided that are particularly suited for reducing degrading audio effects such as zipper noise. In one embodiment, these systems switchably couple an electronic potentiometer between an amplifier's inverting input terminal and interleaved tap points along a resistor that is coupled to the amplifier's output terminal. This arrangement introduces a number of fine gain steps between the gain steps that are realized with adjacent ones of the interleaved tap points to substantially reduce or eliminate zipper noise in a audio system that processes the system's output signal. The interleaved tap points facilitate efficient operation of the potentiometer during gain changes. They also permit the potentiometer to be effectively bypassed between gain changes so that distortion effects are substantially eliminated.