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We have derived theory predicting the impact phase modulation has on dual-pumped parametric amplifiers which includes also the effect of pump power fluctuations. The theory shows that gain perturbations due to perturbations in the pump frequencies can be significantly reduced by operating the two pumps out of phase. Furthermore, filtering the phase-modulated pumps can introduce detrimental gain variations and we propose the use of "flat-top" filter characteristics in order to reduce the filter bandwidths around the pump without causing too much gain-variations on the amplified signal. We also investigate the effect of detuned optical filters.