Increasing demand for energy and reduction of CO2 emissions has revived interest in nuclear energy. Designing materials for radiation environments necessitates fundamental understanding of how radiation-induced defects alter mechanical properties. Ion beams create radiation damage efficiently without material activation, but their limited penetration depth requires small-scale testing. However, strength measurements of nano-scale irradiated specimens have not been previously performed. Here we show that yield strengths approaching macroscopic values are measured from irradiated ~400 nm diameter copper specimens. Quantitative in situ nano-compression testing in a transmission electron microscope reveals that the strength of larger samples is controlled by dislocation-irradiation defect interactions, yielding size-independent strengths. Below ~400 nm, size-dependent strength results from dislocation source limitation. This transition length-scale should be universal, but depend on material and irradiation conditions. We conclude that for irradiated copper, and presumably related materials, nano-scale in situ testing can determine bulk-like yield strengths and simultaneously identify deformation mechanisms.