The influence of chromatic dispersion on continuous-wave (CW)-pumped supercontinuum (SC) generation in kilometer-long standard fibers is experimentally investigated. We perform our study by means of a tunable, high-power fiber ring laser pumping a dispersion-shifted fiber in the wavelength range of small and medium anomalous dispersion. Our results show that, at low input powers, chromatic dispersion plays a dominant role on nonlinear pump spectral broadening, giving rise to a broader spectrum when pumping just above the zero-dispersion wavelength of the fiber. At higher input powers, however, the width of the generated SC spectrum is mostly due to the Raman effect, hence more independent of the value of the chromatic dispersion coefficient. We show that, in this case, the optimum pumping wavelengths for SC generation are not so close to the zero-dispersion wavelength of the fiber as in the previous case. In these conditions, as the chromatic dispersion grows, we can obtain square-shaped and high-power density spectra, which seem extremely promising for applications in optical coherence tomography.