This paper addresses the problem of controlling the envelope’s power peak of single carrier modulated signals, band limited by root-raised cosine (RRC) pulse shaping filters, in order to reduce power amplifier back-off for very small aperture terminals ground stations. Magnitude modulation (MM) is presented as a very efficient solution to the peak-to-average power ratio problem. This paper gives a detailed description of the MM concept and its recent evolutions. It starts by extending the look-up-table (LUT) based approach of the MM concept to M-ary constellations with M ≤ 16. The constellation and RRC symmetries are explored, allowing considerable reduction on LUT computation complex- ity and storage requirements. An effective multistage polyphase (MPMM) approach for the MM concept is then proposed. As opposed to traditional LUT-MM solutions, MM coefficients are computed in real-time by a low complexity multirate filter system. The back-off from high-power amplifier saturation is almost eliminated (reduction is greater than 95%) with just a 2-stage MPMM system even for very demanding roll-off cases (e.g., α = 0.1). Also, the MPMM is independent of modulation in use, allowing its easy application to constellations with M > 16.