Temperature-dependent Hall-effect measurements have been performed on three Ga-doped ZnO thin films of various thicknesses (65, 177, and 283 nm), grown by pulsed laser deposition at 400 °C and annealed at 400 °C for 10 min in Ar, N2, or forming-gas (5% H2 in Ar). The donor ND and acceptor NAconcentrations as a function of sample thickness and annealing conditions are determined by a new formalism that involves only ionized-impurity and boundary scattering. Before annealing, the samples are highly compensated, with ND = (2.8 ± 0.3) × 1020 cm-3 and NA = (2.6 ± 0.2) × 1020 cm-3. After annealing in Ar the samples are less compensated, with ND = (3.7 ± 0.1) × 1020 cm-3 and NA = (2.0 ± 0.1) × 1020 cm-3; furthermore, these quantities are nearly independent of thickness. However, after annealing in N2 and forming-gas, ND and NA are thickness dependent, partly due to depth-dependent diffusion of N2 and H, respectively.