A highly-Ga-doped ZnO (GZO) layer of thickness d grown by molecular-beam epitaxy on an undoped ZnO buffer layer exhibits enhanced mobility μ due to electron diffusion (about 2 nm) from the low-mobility GZO into the high-mobility ZnO. For d = 300 nm, the combined GZO/ZnO structure has Hall mobility μ = 34.2 cm2/V-s, due almost entirely to electrons in the GZO, whereas for d = 50, 25, or 5 nm, μ = 37.0, 43.4, and 64.1 cm2/V-s, respectively, due to the influence of electrons in the ZnO. This observation of an increase of μ with decrease in d is very unusual for thin films of GZO on various substrates. However, Poisson analysis and degenerate scattering theory accurately predict the measured values of μ vs d with no adjustable parameters. For the case d = 5 nm, only 9.7% of the electrons from the GZO diffuse into the ZnO, but those closest to the interface can have μ > 200 cm2/V-s, raising the overall mobility from 34 to 64 cm2/V-s. More complicated structures can produce higher percentages of electrons in the ZnO and thus even higher mobilities. For example, simulation shows that six repeated units of a 1-nm-GZO/2-nm-ZnO structure will have 43% of the electrons in the ZnO and an average mobility of 152 cm2/V-s. This structure has roughly the same conductance as that of a GZO-only layer having the same total thickness (18 nm), but a much lower free-carrier concentration and thus a much higher transmittance in the near IR. This “Debye-tail” technology allows optimization of the conductance/transmittance tradeoff for different applications of transparent conductive oxides.