Significance The emergence of heterogeneous nanostructured metals offers exciting opportunities for achieving extraordinary mechanical properties. Gradient nanotwinned Cu is a prominent class of heterogeneous nanostructured metals, as it exhibits a superior extra strength compared with nongradient counterparts. However, the mechanistic origin of the extra strength remains elusive. At a more fundamental level, the strengthening effects of plastically inhomogeneous deformation in heterogeneous nanostructured metals are not well understood. Here, we use a combination of controlled material processing, back-stress measurement, dislocation microstructure characterization, and strain gradient plasticity modeling to unravel the origin of the extra strength in gradient nanotwinned Cu. The combined experimental and modeling framework may be applied to accelerate the rational design of heterogeneous nanostructured metals with enhanced mechanical performance.