The present invention relates to a hair cosmetic composition for cleansing and conditioning hair fibers, in particular human hair fibers, the hair cosmetic composition comprising anionic surfactants, amphoteric surfactants, thiol-based compounds selected from thiolactic acid, thiolactic acid derivatives, their salts, and mixtures thereof, thickening agents; nonionic surfactants; and water; wherein the pH of the composition ranges from about 2 to less than 7. The invention also concerns a method for imparting hair care benefits to hair fibers such as straightening effects, volume reduction, frizz control, manageability, cosmeticity, and smooth feel, in addition to cleansing and conditioning benefits and a use for hair care employing the cosmetic compositions of the present invention.