We propose a dual-pump third-order nonlinear scheme for producing pairs of correlated photons that is less susceptible to Raman noise than typical spontaneous four-wave mixing (SFWM) methods. Beginning with the full multimode Hamiltonian, we derive a general expression for the joint spectral amplitude, from which the probability of producing a pair of photons can be calculated. As an example, we demonstrate that a probability of 0.012 pairs per pulse can be achieved in an appropriately designed fused silica microfiber. As compared with single pump SFWM in standard fiber, we calculate that our process shows significant suppression of the spontaneous Raman scattering and an improvement in the signal to noise ratio. ; 7 page(s)