Birefringent single-mode fibers with random polarization mode coupling and polarization dependent losses are considered. The effect of these losses on polarization mode dispersion (PMD) is computed. The relevant number is found to be the differential loss between both polarization modes over one coupling length. For polarizing fibers, the coupling length is of several kilometers, the relevant number is thus high, and the PMD is significantly reduced by the differential loss. For standard fibers, on the other hand, the coupling length is of several tens of meters, the relevant number is thus small and polarization dependent losses have a negligible effect on the PMD.