We have performed shell model calculations of the half-lives and neutron-branching probabilities of the r-process waiting-point nuclei at the magic neutron number N = 82. These new calculations use a larger model space than previous shell model studies and an improved residual interaction which is adjusted to recent spectroscopic data around A = 130. Our shell model results give a good account of all experimentally known half-lives and $Q_\beta^-$ values for the N = 82 r-process waiting-point nuclei. Our half-life predictions for the N = 82 nuclei with Z = 42-46 agree well with recent estimates based in the energy-density functional method.