We demonstrate that the Relative Intensity Noise (RIN) of a supercontinuum source can be significantly reduced using the new concept of undertapering, where the fiber is tapered to a diameter that is smaller than the diameter that gives the shortest blue edge, which is typically regarded as the optimum. We show that undertapering allows to control the second zero dispersion wavelength and use it as a soliton barrier to stop the redshifting solitons at a pre-defined wavelength, and thereby strongly reduce the RIN. We demonstrate how undertapering can reduce the spectrally averaged RIN in the optical coherence tomography bands, 500-800nm and 1150-1450nm, by more than a factor two.