It has been successfully demonstrated to compress 5 ps optical pulses down to 20 fs by a 15.1-m-long single-stage step-like dispersion profiled fiber (SDPF) through a series of the higher-order soliton compression processes in conjunction with a single and ordinary erbium-doped fiber preamplifier. The SDPF compressor contains two kinds of dispersion-flattened fibers (DFFs) at its end and was composed by fiber-splicing with an aid of an extremely careful cutback method. In addition, we have compared the measured compression profiles in the 20–100 fs range with simulation results calculated on the bases of a few elementary soliton models and some experimentally extracted parameters, which is aimed to investigate and clarify its compression mechanism. It was found out that the standard nonlinear Schroedinger equation works appropriately to some extent even in the 30–100 fs range for the DFF used here, although some difficulty exists in modeling the pulse width evolution in the sub-30 fs range as far as the parameters that we used are concerned.