The muon capture reactions 2 H(µ − , νµ)nn and 3 He(µ − , νµ) 3 H are studied with conventional or chiral realistic potentials and consistent weak currents. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v18 or chiral N3LO two-nucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A = 3. The weak current consists of polar-and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (χEFT) framework. There is one parameter (either the N -to-∆ axial coupling constant in the meson-exchange model, or the strength of a contact term in the χEFT model) which is fixed by reproducing the Gamow-Teller matrix element in tritium β-decay. The model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the χEFT currents) is weak, resulting in total rates of 392.0 ± 2.3 s −1 for A = 2, and 1484 ± 13 s −1 for A = 3, where the spread accounts for this model dependence.