We demonstrate greatly improved results for the production of correlated photon-pairs using the four-photon scattering process in silica fiber. We achieve a true-coincidence-count to accidental-coincidence-count ratio greater than 10, when the photon-pair production rate is about 0.04/pulse. This represents a four-fold improvement over our previous results. The contribution of spontaneous Raman scattering, the primary cause of uncorrelated photons that degrades the fidelity of this source, is reduced by decreasing the wavelength detuning between the correlated photons and the pump photons and by using polarizers to remove the cross-polarized Raman-scattered photons. Excess Raman scattering could be further suppressed by cooling the silica fiber. Even without cooling the fiber, the achieved 10 to 1 ratio of true-coincidence to accidental-coincidence makes the fiber source of correlated photon-pairs a useful tool for realizing various quantum-communication protocols.