We obtain room-temperature resistivities as low as ρ =1.4 x 10-4 Ω-cm in transparent Ga-doped ZnO grown on Al2O3 by pulsed laser deposition (PLD) at 200 °C in 10 mTorr of pure Ar and then annealed in a Zn environment. Donor ND and acceptor NA concentrations are calculated from a recently developed scattering theory that is valid for any degenerate semiconductor material and requires only two input parameters, mobility μ and carrier concentration n measured at any temperature in the range 5 - 300 K. By comparison with SIMS and positron annihilation measurements, it has been shown that the donors in these samples are mostly GaZn, as expected, but that the acceptors are point defects, Zn vacancies VZn. PLD growth in Ar at 200 °C produces a high concentration of donors [GaZn] = 1.4 x 1021 cm-3, but VZn acceptors are produced at the same time, due to self-compensation. Fortunately, a large fraction of the VZn can be eliminated by annealing in a Zn environment. The theory gives ND and NA, and thus [GaZn] and [VZn], at each step of the growth and annealing process. For convenience, the theory is presented graphically, as plots of μ vs n at various values of compensation ratio K = NA/ND. From the value of K corresponding to the experimental values of μ and n, it is possible to calculate ND = n/(1 - K) and NA = nK/(1 - K).