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.