Several series of epitaxial films of nominal pure and bismuth-, aluminum-substituted yttrium iron garnet are grown on [111]-oriented paramagnetic substrates from PbO-fluxed melts. The growth rate is varied systematically by changing the supercooling. The optical absorption at a wavelength of 1330 nm and the concentrations of the impurities Pb2+, Pb4+, Pt4+, Si4+, and Ca2+ are measured. The absorption shows a minimum at a certain growth rate vmin, which increases linearly with the saturation temperature of the melt. The minimum of the absorption constant reaches values below 0.3 cm−1. The as-grown films contain a surplus of four-valent impurities, the minimum concentration of which correlates with the minimum of the optical absorption. The absorption of samples with growth rates higher than vmin can be reduced considerably by annealing in hydrogen atmosphere at 430 °C for a few minutes.