Output pulses from a photonic crystal fiber (PCF) with a zero-dispersion wavelength (ZDW: 853 nm) were compressed to 5.8 fs by feedback spectral-phase compensation. Furthermore, for another PCF with a shorter ZDW (744 nm), whose output spectral-phase measurement and pulse compression are generally thought to be difficult because of coherence degradation between pulses, we measured successfully their phases in the entire spectral region (480 to 1000 nm) by a suitable selection of input pulse and fiber parameters. The pulse compression experiment using an improved feedback system showed that in the short-wavelength region, pulses can be compressed to 4.9 fs, whereas in the entire spectral region, pulses cannot be compressed. This is because the visibility of the spectral interferogram in the spectral-phase interferometry for direct electric-field reconstruction (SPIDER) signal in the longer-wavelength region corresponding to the phase-sensitive soliton-breaking-up region is degraded by large phase modulation using a spatial light modulator.