Twinning is one of most prevalent deformation mechanisms in materials. Having established a quantitative theory to predict onset twinning stress τcrit in fcc elemental metals from their generalized planar-fault-energy (GPFE) surface, we exemplify its use in alloys where the Suzuki effect (i.e., solute energetically favors residing at and near planar faults) is operative; specifically, we apply it in Cu-xAl (x is 0, 5, and 8.3 at. %) in comparison with experimental data. We compute the GPFE via density-functional theory, and we predict the solute dependence of the GPFE and τcrit, in agreement with measured values. We show that τcrit correlates monotonically with the unstable twin fault energies (the barriers to twin nucleation) rather than the stable intrinsic stacking-fault energies typically suggested. We correlate the twinning behavior and electronic structure with changes in solute content and proximity to the fault planes through charge-density redistribution at the fault and changes to the layer- and site-resolved density of states, where increased bonding charge correlates with decrease in fault energies and τcrit.