Abstract The recent, very accurate proton-proton analyzing-power measurements by the Zürich group at t lab = 50.04 MeV are analyzed. We show that in order to arrive at a proper description of these data, the magnetic-moment interaction has to be included in all partial waves. It is also shown that some of the approximations made in the literature, when trying to incorporate this magnetic-moment interaction, are inadequate. From these beautiful data one can now determine quite accurately the phase shifts at 50 MeV. We compare our results with the phase shifts found in other phase-shift analyses. Some of our phase shifts differ by 6–9 standard deviations from these analyses. Finally, we compare the predictions of some well-known nucleon-nucleon potential models with these high-precision data.