We consider the spin-exchange (SE) cross section in electron scattering from 3 He II, which drives the hyperfine-changing 3.46 cm (8.665 GHz) line transition. Both the analytical quantum defect method -applicable at very low energies -and accurate R-matrix techniques for electron-He + scattering are employed to obtain SE cross sections. The quantum defect theory is also applied to electron collisions with other one-electron ions in order to demonstrate the utility of the method and derive scaling relations. At very low energies, the hyperfine-changing cross sections due to e−He + scattering are much larger in magnitude than for electron collisions with neutral hydrogen, hinting at large rate constants for equilibration. Specifically, we obtain rate coefficients of K(10 K) = 1.10 × 10 −6 cm 3 /s and K(100 K) = 3.49 × 10 −7 cm 3 /s.