High-entropy alloys (HEA) form solid solutions with large chemical disorder and excellent mechanical properties. We investigate the origin of HEA strengthening in face-centered-cubic (fcc) single-phase HEAs through molecular dynamics simulations of dislocations, in particular, the equiatomic CrCoNi, CrMnCoNi, CrFeCoNi, CrMnFeCoNi, FeNi, and, also, Fe0.4Mn0.27Ni0.26Co0.05Cr0.02, Fe0.7Ni0.11Cr0.19. The dislocation correlation length ζ, roughness amplitude Ra, and stacking fault widths WSF are tracked as a function of stress. All alloys are characterized by a well defined depinning stress (σc) and we find a regime where exceptional strength is observed, and a fortuitous combination takes place, of small stacking fault widths and large dislocation roughness Ra. Thus the depinning of two partials seems analogous to unconventional domain wall depinning in disordered magnetic thin films. This regime is identified in specific compositions commonly associated with exceptional mechanical properties (CrCoNi, CrMnCoNi, CrFeCoNi, and CrMnFeCoNi). Yield stress from analytical solute-strengthening models underestimates largely the results in these cases. A possible strategy for increasing strength in multicomponent single-phase alloys is the combined design of stacking fault width and element-based chemical disorder. A hardening factor represents this strategy where combination of low stacking fault and high misfit parameters (and thus high roughness of dislocation at depinning stress) leads to stronger fcc multicomponent alloys.