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The problem of absorption of microwaves by molecular oxygen in the atmosphere is treated by means of a first-order approximation to the impact theory of overlapping spectral lines. By including only the coupling between adjacent rotational states in molecular collisions, we have devised a simple approximate method for computing the interference between lines from measurements on the resolved lines. The need for an empirically determined function describing the linewidth/ pressure ratio is eliminated. Comparisons with measurements at atmospheric pressures show that the first-order interference accounts for the low absorption at the band wings near 1 atm pressure. It also predicts the correct amount of asymmetry between high and low frequency wings. Improvement over previous models for the pressure broadening is obtained at frequencies GHz. This approach is not specific to oxygen and could be adapted to other similar molecules.