Strengthening of metals through nanoscale grain boundaries and coherent twin boundaries is manifested by a maximum strength—a phenomenon known as Hall–Petch breakdown. Different softening mechanisms are considered to occur for nanocrystalline and nanotwinned materials. Here, we report nanocrystalline-nanotwinned Ag materials that exhibit two strength transitions dissimilar from the above mechanisms. Atomistic simulations show three distinct strength regions as twin spacing decreases, delineated by positive Hall–Petch strengthening to grain-boundary-dictated (near-zero Hall–Petch slope) mechanisms and to softening (negative Hall–Petch slope) induced by twin-boundary defects. An ideal maximum strength is reached for a range of twin spacings below 7 nm. We synthesized nanocrystalline-nanotwinned Ag with hardness 3.05 GPa—42% higher than the current record, by segregating trace concentrations of Cu impurity (<1.0 weight (wt)%). The microalloy retains excellent electrical conductivity and remains stable up to 653 K; 215 K better than for pure nanotwinned Ag. This breaks the existing trade-off between strength and electrical conductivity, and demonstrates the potential for creating interface-dominated materials with unprecedented mechanical and physical properties.