From its density the outer core is believed to be an alloy of iron and a light element such as sulfur or oxygen. The nature of the light element in the core is an important constraint for theories of the Earth's formation. In this paper the electronic structures of oxygen and sulfur impurities in metallic iron are investigated to determine if pressure, temperature, and composition-induced changes in bonding might affect phase equilibria along the Fe-FeS and Fe-FeO binaries. The electronic structure of sulfur in metallic iron is consistent with the miscibility between Fe and FeS liquids. Volume compression strengthens the Fe-S bond, and it is expected that at sufficiently high pressure, sulfur can substitute for Fe and give solid solution behavior between Fe and FeS. In contrast, the electronic structure of oxygen in metallic iron shows that oxygen cannot act as a substitutional impurity (replacing Fe). This explains the observed miscibility gap on the Fe-FeO binary at 1 atm pressure. Volume compression does not greatly change the electronic structure if oxygen substitutes for iron in bcc and fcc iron. Iron-oxygen bonding does occur, however, if oxygen occupies interstitial sites. Insofar as the molar volume of FeO incorporated as interstitial oxygen in metallic iron is smaller than that of pure FeO, the incorporation of oxygen into metallic iron may be favored under the pressures of the Earth's core.