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The compression characteristics at femtosecond durations are compared for dispersion-decreasing fibers (DDF's) constructed out of standard step index fibers and fibers designed to have low third-order dispersion (dispersion-flattened fibers). It is shown that the dispersion slope of a standard fiber causes the compressed pulse spectrum to vary substantially with wavelength. Furthermore, the peak of the compressed pulse spectrum can appear in a different wavelength band than the input pulse. Both of these problems are substantially reduced by using a dispersion-flattened DDF. The compression of 3-3.6-ps pulses to durations less than 180 fs was achieved between 1533-1565 nm at a repetition rate of 10 GHz. The shortest pulses obtained were 98 fs with peak-to-pedestal ratios in excess of 20 dB.