We present a model for Saturn's magnetospheric azimuthal plasma velocities measured by Voyager 1 and 2. The observed velocity profiles deviate from full corotation and show two dips slightly outside the orbits of Dione and Rhea. Our velocity model includes as sources for the deviation: radial mass transport, friction between magnetospheric ions and neutrals, and ion pickup. We combine the latter two processes in a quantity called magnetospheric conductance ΣM. We find that inside of 12 Saturn radii (RS) the magnetospheric conductance dominates the slowing of magnetospheric plasma as compared to the effect of radial mass transport. The magnetospheric conductance peaks twice, i.e., slightly outside the orbit of Dione (6.4 RS) and Rhea (8.8 RS), respectively. These two peaks result from a combination of the radially varying magnetic field magnitude, the radial plasma density distribution, and the neutral density distribution. A key finding of our work is that the two magnetospheric conductance maxima can explain the two dips in the observed azimuthal velocity profile that occur at roughly similar locations. Mismatches in the dip locations can be used to retrieve neutral gas profiles. We achieve reasonable agreement with the observations for very small effective Pedersen conductances, ΣI ~ 0.014 S (Voyager 1) and ΣI ~ 0.035 S (Voyager 2) in Saturn's ionosphere, for a total magnetospheric mass source of 40 kg s-1. Larger mass sources require appropriately higher ionospheric conductances. We also find that mass cannot leave, on average, the ≤10 RS regions as plasma. It must be mostly lost via conversion to neutrals.