Offset signals can be designed to have reduced envelope fluctuations allowing high amplification efficiency. When combined with SC-FDE (Single-Carrier with Frequency-Domain Equalization) schemes, they become excellent candidates for broadband wireless systems with severe power constraints. However, the performance of these modulations with conventional FDE receivers is sub-par, even for receivers specifically designed for offset modulations. This is especially serious when large offset QAM (Quadrature Amplitude Modulation) constellations are used. In this paper we consider SC-FDE schemes combined with offset modulations and study the reason behind the poor performance of conventional FDE implementations. We also present pragmatic FDE receivers for offset modulations that have low complexity and excellent performance.