We demonstrate strain-rate sensitivity emerging in single-crystalline Cu nanopillars with diameters ranging from 75 up to 500nm through uniaxial deformation experiments performed at different constant strain rates. In the range of pillar diameters and strain rates tested, we find that the size dependence of the pillar strength deviates from the ubiquitously observed power law to a relatively size-independent flow strength, markedly below the predicted theoretical strength for strain rates slower than 10⁻¹s⁻¹. We find this transition diameter, D_t, to be a function of strain rate, where faster strain rates shift the transition diameter to smaller pillar diameters: D_t∼150nm at 10⁻³s⁻¹ and D_t∼⩽75nm at 10⁻¹s⁻¹. We compute the activation volumes, Ω, as a function of pillar diameter at each strain rate and find that for pillar diameters below D_t, the activation volumes are relatively small, Ω<10b³. This range agrees favorably with atomistic simulations for dislocation nucleation from a free surface. We postulate a plasticity mechanism transition from dislocation multiplication via the operation of truncated dislocation sources, also referred to as single-arm sources, in pillars with diameters greater than D_t to dislocation nucleation from the surface in the smaller samples.