Disclosed herein is an aqueous dye composition for dyeing keratin fibers, for example, human keratin fibers such as the hair, comprising, in a suitable dyeing medium: (a) at least one oxidizing agent, (b) at least one water-insoluble oxygenated organic non-dyeing compound, present in an amount of at least 30% by weight relative to the total weight of the dye composition, and (c) at least one oxidation dye precursor and/or at least one direct dye. Also disclosed herein is a process for dyeing human keratin fibers, for example, the hair, comprising applying such a composition to the keratin fibers.