We analyze the optimal visibility one can obtain in interference experiments with partially polarized light when one acts on only one of the two interfering beams. This is a practical situation that can appear when one does not want to modify or attenuate one of the beams, such as in homodyne detection. It is shown that the optimal configuration usually does not correspond to light with the same degrees of polarization for the two interfering beams. We also demonstrate that a simple interpretation can be obtained with the recently introduced normalized mutual coherence matrix.