A baseband circuit for a communications transmitter includes a baseband modulator, a pulse-shaping filter, and an AMPR reduction circuit. The baseband modulator is configured to generate a sequence of symbols formatted in accordance with a non-constant envelope modulation scheme. The pulse-shaping filter is configured to band-limit the sequence of samples to provide a sequence of samples. The AMPR reduction circuit is configured to analyze and modify one or more samples in the sequence of samples, if a sample in the sequence of samples that has been previously analyzed by the AMPR reduction circuit is determined to have a magnitude less than a predetermined low-magnitude threshold.