In this paper we consider broadband wireless sys- tems with high power efficiency. For this purpose we employ MM (Magnitude Modulation) techniques to reduce the PAPR (Peak- to-Average Power Ratio) of the transmitted signals, allowing efficient power amplification. Designed transceivers combine MM with SC-FDE (Single-Carrier with Frequency-Domain Equaliza- tion) methods upon iterative-block decision feedback equalization (IB-DFE). Since IB-DFE schemes designed for conventional SC signals are not suitable when we employ PAPR-reduction tech- niques, the effect of MM is taken into account on the estimation reliability factor that drives IB-DFE convergence. Results for the new proposed MM-IBDFE transceiver present gains above 1.5dB in the overall power efficiency, even when considering severely time-dispersive channels.