The subject matter of the present Application is cosmetic agents for treating keratinic fibers, which encompass at least two phases present alongside one another but separated from one another by a phase boundary, where the first phase (I) represents an aqueous phase that contains at least one chemical oxidizing agent, and where the second phase (II) represents a hydrophobic oil phase that contains a mixture of isopropyl palmitate (II-1) and at least one further liquid, branched carboxylic acid ester (II-2). The compositions are particularly shelf-stable and cold-stable, and are notable for outstanding care-providing properties.