Interference-reducing circuits include a feed-forward circuit for subtracting all or part of a desired transmitter-signal component from a signal coupled from the power amplifier's output path. The error signal from this feed-forward circuit contains a replica of distortion in the power amplifier output. A cancellation loop adjusts the phase and/or amplitude of this error signal and combines this adjusted error signal with an interference-carrying signal, removing some of the undesired distortion. A spread-spectrum pilot signal is used in one or both loops, to provide a reference signal that can be monitored by an adjustment circuit, which measures the magnitude and/or phase of a spread-spectrum signal that is injected into the interference-carrying signal and, based on that measurement, adjusts the amplitude, phase, and/or delay of the cancellation signal that is added to the interference-carrying signal. This yields a reduced-interference signal in which undesired distortion is reduced.