A novel process for lightening human keratin fibers comprising applying to the fibers at least one anhydrous composition (A) comprising at least one fatty substance and at least one surfactant, at least one composition (B) comprising at least one organic amine having a pKb less than 12, and at least one composition (C) comprising at least one oxidizing agent and leaving the compositions on the fibers for a period of time sufficient to lighten the fibers, and a multi-compartment device or kit, wherein at least one first compartment comprises the at least one anhydrous composition (A), at least one second compartment comprises the at least one composition (B), and at least one third compartment comprises the at least one composition (C).