The noise properties of a supercontinuum can be controlled by modulating the pump with a seed pulse. In this paper, we numerically investigate the influence of seeding with a partially phase coherent weak pulse or continuous wave. We demonstrate that the noise properties of the generated supercontinuum are highly sensitive to the degree of phase noise of the seed and that a nearly coherent seed pulse is needed to achieve a coherent pulse break-up and low noise supercontinuum. The specific maximum allowable linewidth of the seed laser is found to decrease with increasing pump power.