Methods for oxidizing a hydrocarbon to an intermediate oxidation product by utilizing an activated initiator. The initiator is activated by partially oxidizing a first mixture of the initiator and a hydrocarbon, which mixture contains a rather large amount of initiator. The first mixture may even be just initiator. The first mixture, after the partial oxidation, is mixed with a second mixture containing hydrocarbon and a smaller amount of initiator. The second mixture may even contain no initiator at all. The oxidation is continued to a desired degree. Preferably, at least one of the two mixtures, and even more preferably both reaction mixtures contain an oxidation catalyst and an acidic solvent.