Reshaping compositions, methods or processes, and kits-of-parts reshape keratin fibers. The reshaping composition is an aqueous non-reducing, non-oxidizing reshaping composition for keratin fibers having a pH in the range of 7 to 12 and comprises a) one or more alkalizing agents, b) one or more lipophilic compounds being liquid at 25° C. and atmospheric pressure, at a total concentration in the range of 10% to 80% by weight, calculated to the total weight of the composition, c) one or more surfactants, and d) one or more thickening agents being soluble in or mixable with the one or more lipophilic compounds according to b).