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For conventional cyclic prefix (CP)-assisted single-carrier/frequency-domain equalization (SC/FDE) implementations, as well as for orthogonal frequency-division multiplexing (OFDM) implementations, the CP length is known to be selected on the basis of the expected maximum delay spread. Next, the data block size can be chosen to be large enough to minimize the CP overhead, yet small enough to make the channel variation over the block negligible. This paper considers the possibility of reducing the overall CP assistance, when transmitting sequences of SC blocks, while avoiding an excessively long fast Fourier transform window for FDE purposes and keeping good FDE performances through low-complexity, noniterative receiver techniques. These techniques, which take advantage of specially designed frame structures, rely on a basic algorithm for decision-directed correction (DDC) of the FDE inputs when the CP is not long enough to cope with the time-dispersive channel effects. More specifically, we present and evaluate a novel class of reduced-CP SC/FDE schemes, which takes advantage of a special frame structure for replacing "useless" CP redundancy by fully useful channel coding redundancy, with the help of the DDC algorithm. When using the DDC-FDE technique with these especially designed frame structures, the impact of previous decisions, which are not error-free, is shown to be rather small, thereby allowing a power-efficiency advantage (in addition to the obvious bandwidth-efficiency advantage) over conventional block transmission implementations under full-length CP. Additionally, the DDC algorithm is also shown to be useful to improve the power efficiency of these conventional implementations.