  We combine a limited number of accurately measured transition frequencies in
hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and,
as an essential additional ingredient, a generalized least-squares analysis, to
obtain precise and optimal predictions for hydrogen and deuterium transition
frequencies. Some of the predicted transition frequencies have relative
uncertainties more than an order of magnitude smaller than that of the g-factor
of the electron, which was previously the most accurate prediction of QED.
