Estimates of nuclear matrix elements for neutrinoless double beta decay (02) based on the quasiparticle random phase approximations (QRPA) are affected by theoretical uncertainties, which can be substantially reduced by fixing the unknown strength parameter gpp of the residual particle–particle interaction through one experimental constraint—most notably through the two-neutrino double beta decay (22) lifetime. However, it has been noted that the gpp adjustment via 22 data may bring QRPA models in disagreement with independent data on electron capture (EC) and single beta decay (-) lifetimes. Actually, in two nuclei of interest for 02 decay (100Mo and 116Cd), for which all such data are available, we show that the disagreement vanishes, provided that the axial vector coupling gA is treated as a free parameter, with allowance for gA < 1 (strong quenching). Three independent lifetime data (22, EC, -) are then accurately reproduced by means of two free parameters (gpp, gA), resulting in an overconstrained parameter space. In addition, the sign of the 22 matrix element M2 is unambiguously selected (M2 > 0) by the combination of all data. We discuss quantitatively, in each of the two nuclei, these phenomenological constraints and their consequences for QRPA estimates of the 02 matrix elements and their uncertainties.