Spectrally Efficient FDM (SEFDM) signals employs non-orthogonal and overlapping carriers to provide higher spectrum utilization relative to Orthogonal FDM signals (OFDM). Complex detectors are employed to extract the signal from the intercarrier interference (ICI) created by the loss of orthogonality. Sphere Decoder (SD) is proposed for SEFDM detection as an algorithm that achieves ML bit error rate (BER) performance. However, SD complexity is variable depending on the noise as well as the conditioning of the system. In this paper, the use of Fixed complexity Sphere Decoder (FSD) for the detection of SEFDM signal is proposed. The FSD is more suitable for hardware implementation as it eradicates the variable complexity characteristic of the Sphere Decoder algorithm whilst providing competitive bit error rate (BER) performance. The paper shows how the FSD can be applied to detect SEFDM signals and investigate the performance of the FSD in terms of the bit error rate (BER). Simulations results show that the FSD results in minor error penalties that can be traded-off with complexity.