Spectrally Efficient Frequency Division Multiplexing (SEFDM) is a non-orthogonal multi-carrier communication technique that can pack more sub-carriers than Orthogonal Frequency Division Multiplexing (OFDM) for a given bandwidth. In this paper, we propose a hybrid soft Iterative Detection (ID) together with Fixed Sphere Decoding (FSD) for QAM modulation schemes from 4QAM to 16QAM. In terms of 4QAM, we show that for signaling rates of up to 25 percent, our system can achieve the same performance as OFDM. In terms of 16QAM, we show that given the same complexity, the performance of the ID-FSD detector outperforms our previous detector by 1.6 dB.