A study of fatigue hardening in single crystals of pure copper shows that, before saturation, stress-strain loops can display workhardening rates of about a third of the elastic shear modulus. These rates exceed tensile workhardening rates by roughly two orders of magnitude. This suggests that there is a large volume fraction of obstacles to plastic flow which are essentially non-deformable and give rise to inclusion stresses of considerable magnitude. The much lower hardening rates in cycles after saturation when persistent slip bands have formed suggest a lower volume fraction of obstacles, as is observed by transmission electron microscopy. A simple composite model involving an inclusion stress, a bowing stress and a passing, stress accounts for the workhardening rates semi-quantitatively in terms of observed dislocation microstructures. Possible implications for polycrystals are considered.