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For conventional CP-assisted (Cyclic Prefix) block transmission systems, the CP length is selected according to the expected maximum delay spread. In this paper, an SDDC-aided (Soft Decision Directed Correction), iterative FDE (Frequency Domain Equalization) technique is presented for reduced-CP, SC-based (Single Carrier) block transmission systems using conventional frame structures. A more sophisticated Turbo SDDC-FDE technique is then proposed for improved performances in such systems, through a moderately increased complexity. The relations with some already known iterative FOE techniques are established, and a set of performance results is used to show the advantages of the SDDC-aided approach, namely the following: the fact that it can operate in an acceptable way even when, for the sake of implementation simplicity, no decoding operations are used to improve the iterative FDE process; the possibility of achieving the maximum power efficiency gain that a strong CP reduction allows.